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|Ab urbe condita||2158|
|Balinese saka calendar||1326–1327|
|English Regnal year||6 Hen. 4 – 7 Hen. 4|
|Chinese calendar||甲申年 (Wood Monkey)|
4101 or 4041
— to —
乙酉年 (Wood Rooster)
4102 or 4042
|- Vikram Samvat||1461–1462|
|- Shaka Samvat||1326–1327|
|- Kali Yuga||4505–4506|
|Japanese calendar||Ōei 12|
|Minguo calendar||507 before ROC|
|Thai solar calendar||1947–1948|
1531 or 1150 or 378
— to —
1532 or 1151 or 379
|Wikimedia Commons has media related to 1405.|
- May 29 – In England, Ralph Neville, 1st Earl of Westmorland, meets Archbishop Richard le Scrope of York and Earl of Norfolk Thomas Mowbray in Shipton Moor, tricks them to send their rebellious army home, and then imprisons them.
- June 8 – Archbishop Richard le Scrope of York and Thomas Mowbray, Earl of Norfolk, are executed in York on Henry IV's orders.
- July 11 – Ming Dynasty fleet commander Zheng He sets sail from Suzhou, to explore the world for the first time.
- October 5 – Christine de Pizan writes a letter to Queen Isabeau, urging her to intervene in the political struggle between the dukes of Burgundy and Orléans.
- November 17 – The Sultanate of Sulu is established on the Sulu Archipelago, off the coast of Mindanao in the Philippines.
- Bath Abbey is built in England.
- The first record is written of whiskey being consumed in Ireland, where it is distilled by Catholic monks.
- Bellifortis, a book on military technology, is published by Konrad Kyeser.
- Christine de Pizan writes The Book of the City of Ladies.
- February 8 – Constantine XI, last Byzantine Emperor (d. 1453)
- February 22 – Gilbert Kennedy, 1st Lord Kennedy, Scottish noble (d. 1489)
- March 6 – King John II of Castile (d. 1454)
- May 6 – George Kastrioti, better known as Skanderbeg, Albanian national hero (d. 1468) (probable date)
- October 18 – Pope Pius II (d. 1464)
- date unknown – Louis I, Count of Montpensier (d. 1486)
- January 12 – Eleanor Maltravers, English noblewoman (b. 1345)
- February 14 – Timur (aka Tamerlane), Turco-Mongol monarch and conqueror (b. 1336)
- March 16 – Margaret III, Countess of Flanders (b. 1350)
- April 19 – Thomas West, 1st Baron West (b. 1335)
- May 29 – Philippe de Mézières, advisor to Charles V of France
- June 8
- June 20 – Alexander Stewart, Earl of Buchan, fourth son of King Robert II of Scotland (b. 1343)
- probable – Jean Froissart, French chronicler (b. 1337)