The son of Sir Banks Jenkinson, 4th Baronet, and Catherine Dashwood.
[2] He was educated at John Roysse's Free School in Abingdon, (now Abingdon School) and later St John's College, Oxford and was awarded an Honorary Master of Arts degree;[3] matriculated 31 May 1738 aged 17.
[2] He earned a Doctor of Civil Law on 17 April 1749 but it is unknown if he practiced.
[4] He succeeded his father Sir Banks Jenkinson, 4th Baronet, to the title on 2 July 1738.
He died on 8 August 1766, aged 46 and was succeeded by Sir Banks Jenkinson, 6th Baronet.