5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has attained significance throughout history in part because typical humans have five digits on each hand.

← 4 5 6 →
-1 0 1 2 3 4 5 6 7 8 9
Numeral systemquinary
Greek numeralΕ´
Roman numeralV, v
Greek prefixpenta-/pent-
Latin prefixquinque-/quinqu-/quint-
Greekε (or Ε)
Arabic, Kurdish٥
Persian, Sindhi, Urdu۵
Chinese numeral五,伍
Korean numerals다섯,오

In mathematicsEdit

Five is the third smallest prime number.[1] Since it can be written as 22 + 1, five is classified as a Fermat prime;[1] therefore, a regular polygon with 5 sides (a regular pentagon) is constructible with compass and an unmarked straightedge. Five is the third Sophie Germain prime,[1] the first safe prime, the third Catalan number,[2] and the third Mersenne prime exponent.[3] Five is the first Wilson prime and the third factorial prime, also an alternating factorial.[4] Five is the first good prime.[5] It is an Eisenstein prime with no imaginary part and real part of the form 3p − 1.[1] It is also the only number that is part of more than one pair of twin primes. Five is also a super-prime, and a congruent number.[6]

Five is conjectured to be the only odd untouchable number,[7] and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.

Five is also the only prime that is the sum of two consecutive primes, namely 2 and 3, with these indeed being the only possible set of two consecutive primes.

The number 5 is the fifth Fibonacci number, being 2 plus 3.[1] It is the only Fibonacci number that is equal to its position. Five is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... (OEISA030452 lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.[8]

5 is the length of the hypotenuse of the smallest integer-sided right triangle.

In bases 10 and 20, 5 is a 1-automorphic number.

Five is the second Sierpinski number of the first kind, and can be written as S2 = (22) + 1.[9]

While polynomial equations of degree 4 and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel–Ruffini theorem. This is related to the fact that the symmetric group Sn is a solvable group for n ≤ 4 and not solvable for n ≥ 5.

While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar: K5, the complete graph with 5 vertices.

There are five known unitary perfect numbers. A sixth unitary number, if discovered, would have at least nine odd prime factors.[10]

There are five Platonic solids.[11] There are also five cell-transitive space-filling parallelohedra,[12] five regular uniform polyhedron compounds,[13] and five abstract polyhedra.[14]

There are five regular honeycombs in hyperbolic 5-space; all are paracompact solutions with infinite facets and vertex figures.[15]

A polygon with five sides is a pentagon. Figurate numbers representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.

Five is the only prime number to end in the digit 5 because all other numbers written with a 5 in the ones place under the decimal system are multiples of five. As a consequence of this, 5 is in base 10 a 1-automorphic number.

Vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions, unlike expansions with all other prime denominators, because they are prime factors of ten, the base. When written in the decimal system, all multiples of 5 will end in either 5 or 0.

There are five non-supersingular primes (37, 43, 53, 61, and 67) smaller than the largest prime divisor of the Monster group, 71.[16] All primes greater than 71 are non-supersingular.

There are five exceptional Lie groups.

List of basic calculationsEdit

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5 × x 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5 ÷ x 5 2.5 1.6 1.25 1 0.83 0.714285 0.625 0.5 0.5 0.45 0.416 0.384615 0.3571428 0.3
x ÷ 5 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5x 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125
x5 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 248832 371293 537824 759375

In the powers of 5, every power ends with the number five and from 53, if the exponent is odd, then the hundreds digit is 1; instead, if it is even, the hundreds digit is 6.

In decimal notation, n5 always ends in the same digit as n.

Evolution of the Arabic digitEdit

The evolution of the modern Western digit for the numeral 5 cannot be traced back to the Indian system, as for the digits 1 to 4. The Kushana and Gupta empires in what is now India had among themselves several different forms that bear no resemblance to the modern digit. The Nagari and Punjabi took these digits and all came up with forms that were similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the digit in several different ways, producing from that were more similar to the digits 4 or 3 than to 5.[17] It was from those digits that Europeans finally came up with the modern 5.

While the shape of the character for the digit 5 has an ascender in most modern typefaces, in typefaces with text figures the glyph usually has a descender, as, for example, in  .




  • There are generally considered to be five senses.
  • Almost all amphibians, reptiles, and mammals which have fingers or toes have five of them on each extremity.[24]


Religion and cultureEdit


  • The god Shiva has five faces[26] and his mantra is also called panchakshari (five-worded) mantra.
  • The goddess Saraswati, goddess of knowledge and intellectual is associated with panchami or the number 5.
  • There are five elements in the universe according to Hindu cosmology: dharti, agni, jal, vayu evam akash (earth, fire, water, air and space respectively).
  • The most sacred tree in Hinduism has 5 leaves in every leaf stunt.[clarification needed]
  • Most of the flowers have 5 petals in them.
  • The epic Mahabharata revolves around the battle between Duryodhana and his 99 other brothers and the 5 pandava princes—Dharma, Arjuna, Bhima, Nakula and Sahadeva.






  • The five sacred Sikh symbols prescribed by Guru Gobind Singh are commonly known as panj kakars or the "Five Ks" because they start with letter K representing kakka (ਕ) in the Punjabi language's Gurmukhi script. They are: kesh (unshorn hair), kangha (the comb), kara (the steel bracelet), kachhehra (the soldier's shorts), and kirpan (the sword) (in Gurmukhi: ਕੇਸ, ਕੰਘਾ, ਕੜਾ, ਕਛਹਰਾ, ਕਿਰਪਾਨ).[34] Also, there are five deadly evils: kam (lust), krodh (anger), moh (attachment), lobh (greed), and ankhar (ego).


Other religions and culturesEdit

Art, entertainment, and mediaEdit

Fictional entitiesEdit




Other usesEdit





  • The Olympic Games have five interlocked rings as their symbol, representing the number of inhabited continents represented by the Olympians (Europe, Asia, Africa, Australia and Oceania, and the Americas).[76]
  • In AFL Women's, the top level of women's Australian rules football, each team is allowed 5 "interchanges" (substitute players), who can be freely substituted at any time.
  • In baseball scorekeeping, the number 5 represents the third baseman's position.
  • In basketball:
    • The number 5 is used to represent the position of center.
    • Each team has five players on the court at a given time. Thus, the phrase "five on five" is commonly used to describe standard competitive basketball.[77]
    • The "5-second rule" refers to several related rules designed to promote continuous play. In all cases, violation of the rule results in a turnover.
    • Under the FIBA (used for all international play, and most non-US leagues) and NCAA women's rule sets, a team begins shooting bonus free throws once its opponent has committed five personal fouls in a quarter.
    • Under the FIBA rules, A player fouls out and must leave the game after committing five fouls
  • Five-a-side football is a variation of association football in which each team fields five players.[78]
  • In ice hockey:
    • A major penalty lasts five minutes.[79]
    • There are five different ways that a player can score a goal (teams at even strength, team on the power play, team playing shorthanded, penalty shot, and empty net).[80]
    • The area between the goaltender's legs is known as the five-hole.[81]
  • In most rugby league competitions, the starting left wing wears this number. An exception is the Super League, which uses static squad numbering.
  • In rugby union:


  • 5 is the most common number of gears for automobiles with manual transmission.[83]
  • In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.[84]
  • On almost all devices with a numeric keypad such as telephones, computers, etc., the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it useful to be able to feel the keys of a telephone. All other numbers can be found with their relative position around the 5 button (on computer keyboards, the 5 key of the numpad has the raised dot or bar, but the 5 key that shifts with % does not).[85]
  • On most telephones, the 5 key is associated with the letters J, K, and L,[86] but on some of the BlackBerry phones, it is the key for G and H.
  • The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.[87]
  • The resin identification code used in recycling to identify polypropylene.[88]

Miscellaneous fieldsEdit

The fives of all four suits in playing cards

Five can refer to:

See alsoEdit


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  3. ^ Weisstein, Eric W. "Mersenne Prime". mathworld.wolfram.com. Retrieved 2020-07-30.
  4. ^ Weisstein, Eric W. "Twin Primes". mathworld.wolfram.com. Retrieved 2020-07-30.
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  6. ^ Sloane, N. J. A. (ed.). "Sequence A003273 (Congruent numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  7. ^ Pomerance, Carl. "On Untouchable Numbers and Related Problems" (PDF). Dartmouth College.
  8. ^ Weisstein, Eric W. "Perrin Sequence". mathworld.wolfram.com. Retrieved 2020-07-30.
  9. ^ Weisstein, Eric W. "Sierpiński Number of the First Kind". mathworld.wolfram.com. Retrieved 2020-07-30.
  10. ^ Richard K. Guy (2004). Unsolved Problems in Number Theory. Springer-Verlag. pp. 84–86. ISBN 0-387-20860-7.
  11. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 61
  12. ^ Alexandrov, A. D. (2005). "8.1 Parallelohedra". Convex Polyhedra. Springer. pp. 349–359.
  13. ^ Skilling, John (1976). "Uniform Compounds of Uniform Polyhedra". Mathematical Proceedings of the Cambridge Philosophical Society. 79: 447–457. doi:10.1017/S0305004100052440. MR 0397554.
  14. ^ Wills, J. M. (1987). "The combinatorially regular polyhedra of index 2". Aequationes Mathematicae. 34: 206–220. doi:10.1007/BF01830672.
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  17. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 394, Fig. 24.65
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  19. ^ Cinalli, G.; Maixner, W. J.; Sainte-Rose, C. (2012-12-06). Pediatric Hydrocephalus. Springer Science & Business Media. p. 19. ISBN 978-88-470-2121-1. The five appendages of the starfish are thought to be homologous to five human buds
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  22. ^ Pugh, Philip (2011-11-02). Observing the Messier Objects with a Small Telescope: In the Footsteps of a Great Observer. Springer Science & Business Media. p. 44. ISBN 978-0-387-85357-4. M5, like the previous objects in the Messier Catalogue is a globular star cluster in Serpen
  23. ^ Ford, Dominic. "The galaxy NGC 5". In-The-Sky.org. Retrieved 2020-08-02.
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  25. ^ Pozrikidis, Constantine (2012-09-17). XML in Scientific Computing. CRC Press. p. 209. ISBN 978-1-4665-1228-3. 5 5 005 ENQ (enquiry)
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  38. ^ Walsh, Len (2008-11-15). Read Japanese Today: The Easy Way to Learn 400 Practical Kanji. Tuttle Publishing. ISBN 978-1-4629-1592-7. The Japanese names of the days of the week are taken from the names of the seven basic nature symbols
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  40. ^ Allcroft, Britt; Friends, Thomas &; Awdry, W. (2014). James the Splendid Red Engine. Egmont UK Limited. ISBN 978-1-4052-7506-4. Meet Sodor's number 5 engine
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  43. ^ Windham, Ryder (2008). Indiana Jones Collector's Edition. Scholastic. p. 298. ISBN 978-0-545-09183-1. he gave him the five sacred stones with magical properties
  44. ^ Chance, Jane (2016-11-21). Tolkien, Self and Other: "This Queer Creature". Springer. p. 70. ISBN 978-1-137-39896-3. These five included the head wizard,
  45. ^ Jacoby, Henry (2012-02-23). Game of Thrones and Philosophy: Logic Cuts Deeper Than Swords. John Wiley & Sons. p. 34. ISBN 978-1-118-20605-8. ...view the events of A Song of Ice and Fire. As we'll see, the War of the Five Kings
  46. ^ Netflix; Way, Gerard; Ba, Gabriel (2020). The Making of the Umbrella Academy. Dark Horse Comics. p. 21. ISBN 978-1-5067-1357-1.
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  52. ^ Figes, Orlando (2014-02-11). Natasha's Dance: A Cultural History of Russia. Henry Holt and Company. ISBN 978-1-4668-6289-0. Also sometimes referred to as 'The Mighty Five' or 'Mighty Handful': Balakirev, Rimsky Korsakov, Borodin, Cui and Musorgsky
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  83. ^ Poulton, Mark L. (1997). Fuel Efficient Car Technology. Computational Mechanics Publications. p. 65. ISBN 978-1-85312-447-1. The 5 - speed manual gearbox is likely to remain the most common type
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  88. ^ Stevens, E. S. (2020-06-16). Green Plastics: An Introduction to the New Science of Biodegradable Plastics. Princeton University Press. p. 45. ISBN 978-0-691-21417-7. polypropylene 5
  89. ^ Corporation, Bonnier (1937). Popular Science. Bonnier Corporation. p. 32. ...another picture of one of the world's most famous babies was made. Fred Davis is official photographer of the Dionne quintuplets...
  90. ^ Smith, Rich (2010-09-01). Fifth Amendment: The Right to Fairness. ABDO Publishing Company. p. 20. ISBN 978-1-61784-256-6. Someone who stands on his or her right to avoid self incrimination is said in street language to be “taking the Fifth,” or “pleading the Fifth.”
  91. ^ Veith (Jr.), Gene Edward; Wilson, Douglas (2009). Omnibus IV: The Ancient World. Veritas Press. p. 52. ISBN 978-1-932168-86-0. The most common accentual-syllabic lines are five-foot iambic lines (iambic pentameter)
  92. ^ Kronland-Martinet, Richard; Ystad, Sølvi; Jensen, Kristoffer (2008-07-19). Computer Music Modeling and Retrieval. Sense of Sounds: 4th International Symposium, CMMR 2007, Copenhagen, Denmark, August 2007, Revised Papers. Springer. p. 502. ISBN 978-3-540-85035-9. Plato and Aristotle postulated a fifth state of matter, which they called "idea" or quintessence" (from "quint" which means "fifth")
  93. ^ Roads, United States Congress Senate Committee on Public Works Subcommittee on (1970). Designating Highway U.S. 50 as Part of the Interstate System, Nevada: Hearings, Ninety-first Congress, First Session; Carson City, Nevada, October 6, 1969; [and] Ely, Nevada, October 7, 1969. U.S. Government Printing Office. p. 78.
  94. ^ Sonderman, Joe (2010). Route 66 in New Mexico. Arcadia Publishing. p. 7. ISBN 978-0-7385-8029-6. North - south highways got odd numbers , the most important ending in 5
  95. ^ Marcus, Jacqueline B. (2013-04-15). Culinary Nutrition: The Science and Practice of Healthy Cooking. Academic Press. p. 55. ISBN 978-0-12-391883-3. There are five basic tastes: sweet, salty, sour, bitter and umami...
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  97. ^ Lazarus, Richard J. (2020-03-10). The Rule of Five: Making Climate History at the Supreme Court. Harvard University Press. p. 252. ISBN 978-0-674-24515-0. ...Justice Brennan's infamous "Rule of Five,"
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