Francis Godolphin Osborne, 5th Duke of Leeds (29 January, 1751 - 31 January, 1799, was a British politician.

He was educated at Westminster School and at Christ Church, Oxford. He was a member of parliament in 1774 and 1775; in 1776 having received a writ of acceleration as Baron Osborne , he entered the House of Lords, and in 1777 Lord Chamberlain of the Queen's Household. In the House of Lords he was prominent as a determined foe of the prime minister, Lord North, who, after he had resigned his position as chamberlain, deprived him of the office of lord lieutenant of the East Riding of Yorkshire in 1780. He regained this, however, two years later. Early in 1783 the Marquess of Carmarthen, as he was called until he succeeded his father in 1789, was selected as ambassador to France, but he did not take up this appointment, becoming instead Secretary of State for Foreign Affairs under William Pitt in December of the same year. As secretary he was little more than a cipher, and he left office in April 1791. Subsequently he took little part in politics, and he died in London. His Political Memoranda were edited by Oscar Browning for the Camden Society in 1884, and there are eight volumes of his official correspondence in the British Museum. His first wife was Amelia (1754—1784), daughter of Robert Darcy, 4th Earl of Holdernesse, who became Baroness Conyers in her own right in 1778. Their elder son, George William Frederick (1775—1838), succeeded his father as duke of Leeds and his mother as Baron Conyers.

|- style="text-align: center;" | width="30%" |Preceded by:
The Earl Temple | width="40%" style="text-align: center;" |Foreign Secretary
1783–1791 | width="30%" |Succeeded by:
The Lord Grenville