| 64621 | June 5 | Holiday and observance | Arbor Day (New Zealand) |
| 64622 | June 5 | Holiday and observance | Constitution Day (Denmark) |
| 64623 | June 5 | Holiday and observance | Constitution Day (Faroe Island) |
| 64624 | June 5 | Holiday and observance | Father's Day (Denmark) |
| 64625 | June 5 | Holiday and observance | Feast of Núr, the first day of the fifth month of the Bahá'í calendar. (Bahá'í Faith) (Only if Bahá'í Naw-Rúz falls on March 21.) |
| 64626 | June 5 | Holiday and observance | Indian Arrival Day (Suriname) |
| 64627 | June 5 | Holiday and observance | Khordad Movement Anniversary (Iran) |
| 64628 | June 5 | Holiday and observance | Liberation Day (Seychelles) |
| 64629 | June 5 | Holiday and observance | President's Day (Equatorial Guinea) |
| 64630 | June 5 | Holiday and observance | Teachers' Day (Romania) |
| 64631 | June 5 | Holiday and observance | World Environment Day (International) |
| 64632 | June 6 | Event | 1508 – Maximilian I, Holy Roman Emperor, is defeated in Friuli by Venetian troops |
| 64633 | June 6 | Event | 1513 – Italian Wars: Battle of Novara. Swiss troops defeat the French under Louis II de la Trémoille, forcing the French to abandon Milan. Duke Massimiliano Sforza is restored. |
| 64634 | June 6 | Event | 1523 – Gustav Vasa, the Swedish regent, is elected King of Sweden, marking a symbolic end to the Kalmar Union. This is the Swedish national day. |
| 64635 | June 6 | Event | 1586 – Francis Drake's forces raid St. Augustine in Spanish Florida. |
| 64636 | June 6 | Event | 1644 – The Qing dynasty Manchu forces led by the Shunzhi Emperor capture Beijing during the collapse of the Ming dynasty. |
| 64637 | June 6 | Event | 1654 – Queen Christina abdicates the Swedish throne and is succeeded by her cousin Charles X Gustav. |
| 64638 | June 6 | Event | 1674 – Shivaji, founder of the Maratha Empire, is crowned. |
| 64639 | June 6 | Event | 1683 – The Ashmolean Museum in Oxford, England, opens as the world's first university museum. |
| 64640 | June 6 | Event | 1749 – The Conspiracy of the Slaves in Malta is discovered. |
| 64641 | June 6 | Event | 1752 – A devastating fire destroys one-third of Moscow, including 18,000 homes. |
| 64642 | June 6 | Event | 1762 – Seven Years' War: British forces begin a siege of Havana, Cuba, and temporarily capture the city in the Battle of Havana. |
| 64643 | June 6 | Event | 1808 – Napoleon's brother, Joseph Bonaparte, is crowned King of Spain. |
| 64644 | June 6 | Event | 1809 – Sweden promulgates a new Constitution, which restores political power to the Riksdag of the Estates after 20 years of enlightened absolutism. At the same time, Charles XIII is elected to succeed Gustav IV Adolf as King of Sweden. |
| 64645 | June 6 | Event | 1813 – War of 1812: Battle of Stoney Creek: A British force of 700 under John Vincent defeats an American force twice its size under William Winder and John Chandler. |
| 64646 | June 6 | Event | 1822 – Alexis St. Martin is accidentally shot in the stomach, leading to William Beaumont's studies on digestion. |
| 64647 | June 6 | Event | 1832 – The June Rebellion in Paris is put down by the National Guard. |
| 64648 | June 6 | Event | 1833 – Andrew Jackson becomes the first U.S. President to ride on a train. |
| 64649 | June 6 | Event | 1844 – The Young Men's Christian Association (YMCA) is founded in London. |
| 64650 | June 6 | Event | 1857 – Sophia of Nassau marries the future King Oscar II of Sweden–Norway. |