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Born 1751.
There is a christening record dated 9th July 1751 at St John the Baptist, Finsbury for Israel Wilkes Booth born 12th May 1751.
Died 1817.
London Deaths & Burials records 1813-1900 for St John, Clerkenwell has an entry dated 11th October 1817 for Wilkes Booth aged 65 years.

Grimwade’s speculation that the John Booth (Grimwade p.445) who entered a maker’s mark in partnership in 1810 was his son is shown to be correct by the christening record in 1788 at St Andrew, Holborn for John Wilkes Booth son of Wilkes and Hannah and the Indentures signed in 1802 for John the son of Wilkes, silversmith of Albermarle Street, Clerkenwell as the apprentice of George Fuller, Stationer.

MCB wrote:Born 1751.
There is a christening record dated 9th July 1751 at St John the Baptist, Finsbury for Israel Wilkes Booth born 12th May 1751.

I may have missed something here which would be nothing new, but on the next page after Israel Wilkes Booth's birth and christening record there is a record for Wilkes Booth who was born to John and Elizabeth Booth on February 1 and baptized on February 12, 1753.

No burial of Israel Wilkes Booth is recorded at St John the Baptist prior to the February 1753 christening of Wilkes Booth. This would be more usual if Israel Wilkes' parents gave the name Wilkes to another of their children.
Both births would generally match the age of around 65 years in 1817 recorded at burial. It is safe to say that Wilkes Booth was born 1751-3.

For accuracy only, Wilkes Booth's baptism was February 19 instead of February 12. I misinterpreted the handwritten number nine.

Wilkes’s brother Richard Booth (1759-1839) a lawyer had several children one of whom was Junius Brutus Booth (1796-1852) who emigrated to the United States where he became the most celebrated American actor of his generation. By his second wife Junius Brutus’s son John Wilkes Booth (1838-1865) assassinated President Abraham Lincoln at Ford’s Theatre Washington on 14 April 1865.
Information courtesy of Peter Cameron