| 5551 | January 13 | Event | 1964 – Anti-Muslim riots break out in Calcutta, resulting in 100 deaths. |
| 5552 | January 13 | Event | 1964 – Karol Wojtyla, the future Pope John Paul II, is appointed archbishop of Kraków, Poland. |
| 5553 | January 13 | Event | 1966 – Robert C. Weaver becomes the first African American Cabinet member when he is appointed United States Secretary of Housing and Urban Development. |
| 5554 | January 13 | Event | 1968 – Johnny Cash performs live at Folsom State Prison |
| 5555 | January 13 | Event | 1972 – Prime Minister Kofi Abrefa Busia and President Edward Akufo-Addo of Ghana are ousted in a bloodless military coup by Colonel Ignatius Kutu Acheampong. |
| 5556 | January 13 | Event | 1974 – Seraphim is elected Archbishop of Athens and All Greece. |
| 5557 | January 13 | Event | 1978 – United States Food and Drug Administration requires all blood donations to be labeled "paid" or "volunteer" donors. |
| 5558 | January 13 | Event | 1982 – Shortly after takeoff, Air Florida Flight 90, a Boeing 737 jet crashes into Washington, D.C.'s 14th Street Bridge and falls into the Potomac River, killing 78 including four motorists. |
| 5559 | January 13 | Event | 1985 – A passenger train plunges into a ravine in Ethiopia, killing 428 in the worst railroad disaster in Africa. |
| 5560 | January 13 | Event | 1986 – A month-long violent struggle begins in Aden, South Yemen between supporters of Ali Nasir Muhammad and Abdul Fattah Ismail, resulting in thousands of casualties. |
| 5561 | January 13 | Event | 1988 – Lee Teng-hui becomes the first native Taiwanese President of the Republic of China. |
| 5562 | January 13 | Event | 1990 – a seven-day pogrom breaks out against the Armenian civilian population of Baku, Azerbaijan during which Armenians were beaten, tortured, murdered, and expelled from the city. |
| 5563 | January 13 | Event | 1990 – Douglas Wilder becomes the first elected African American governor as he takes office in Richmond, Virginia. |
| 5564 | January 13 | Event | 1991 – Soviet Union troops attack Lithuanian independence supporters in Vilnius, killing 14 people and wounding 1000. |
| 5565 | January 13 | Event | 1993 – Space Shuttle program: Endeavour heads for space for the third time as STS-54 launches from the Kennedy Space Center. |
| 5566 | January 13 | Event | 2000 – Bill Gates resigns as CEO of Microsoft. |
| 5567 | January 13 | Event | 2001 – An earthquake hits El Salvador, killing more than 800. |
| 5568 | January 13 | Event | 2012 – The passenger cruise ship Costa Concordia sinks off the coast of Italy. There are 32 confirmed deaths amongst the 4232 passengers and crew. |
| 5569 | January 13 | Event | 2012 – The opening ceremony of the Winter Youth Olympics takes place in Innsbruck, Austria. |
| 5570 | January 13 | Birth | 1334 – Henry II of Castile (d. 1379) |
| 5571 | January 13 | Birth | 1505 – Joachim II Hector, Elector of Brandenburg (d. 1571) |
| 5572 | January 13 | Birth | 1562 – Mark Alexander Boyd, Scottish poet and soldier (d. 1601) |
| 5573 | January 13 | Birth | 1596 – Jan van Goyen, Dutch painter (d. 1656) |
| 5574 | January 13 | Birth | 1610 – Archduchess Maria Anna of Austria (d. 1665) |
| 5575 | January 13 | Birth | 1616 – Antoinette Bourignon, French-Flemish mystic and author (d. 1680) |
| 5576 | January 13 | Birth | 1651 – Henry Booth, 1st Earl of Warrington, English soldier and politician, Chancellor of the Exchequer (d. 1694) |
| 5577 | January 13 | Birth | 1683 – Christoph Graupner, German harpsichord player and composer (d. 1760) |
| 5578 | January 13 | Birth | 1720 – Richard Hurd, English bishop (d. 1808) |
| 5579 | January 13 | Birth | 1749 – Maler Müller, German poet, painter, and playwright (d. 1825) |
| 5580 | January 13 | Birth | 1787 – John Davis, American lawyer and politician, 14th Governor of Massachusetts (d. 1854) |