- May 9 Explorer Alexander Mackenzie sets out on his second expedition to the Pacific from Fort Fork (arrives at Pacific 22nd July)
- May 15 Diego Marín Aguilera flies a glider for "about 360 metres", at a height of 5-6 metres, one of the first attempted flights
- May 19 Netherlands captures French island of St Maarten (held until 1795)
- May 21 Curacao Island Council forbids criticism of House of Orange
- May 25 Father Stephen Theodore Badin is 1st US Roman Catholic priest ordained
- May 30 Georges Couthon chosen member of French Committee the Salut Public