Heneage Finch, 5th Earl of Winchilsea FSA (1657 – 30 September 1726) was an English peer, styled Hon. Heneage Finch until 1712. He was the son of Heneage Finch, 3rd Earl of Winchilsea and Mary Seymour.
The Finch family were traditional royalists. At the Restoration King Charles II recommended Winchelsea to be ambassador to the Porte. He arrived at Constantinople on 17 January 1661. He was eventually recalled by letter on 19 December 1667. He did not leave Turkey until early 1669.
In 1683, he was appointed a Groom of the Bedchamber to the Duke of York and a captain in the Duke's Halberdiers, and was created a D.C.L of Oxford. In 1685, he retained his appointment as Groom of the Bedchamber when York succeeded as James II, was commissioned a colonel, and appointed a deputy lieutenant for Kent. He represented Hythe in James' only Parliament. He lost his posts upon the deposition of James.
He inherited the earldom from his nephew Charles Finch, 4th Earl of Winchilsea in 1712. He refused to take the Oath of Allegiance and declined his seat in the House of Lords. Chosen a FSA in 1724, he died in 1726. Having had no children by his wife, Anne Kingsmill (1661–1720), he was succeeded by his half-brother John.