I would plump for Peter Shilton, at the end of his career (1995-1996) he played for Plymouth Argyle, Wimbledon, Bolton Wanderers, Coventry City, West Ham United and Leyton Orient.
https://en.wikipedia.org/wiki/Peter_Shilton
Peter Leslie Shilton MBE, OBE (born Leicester, England, 18 September 1949) is a former football goalkeeper who holds the record for playing more games than any other player.
In a 30-year career, which included eight different clubs, three World Cups, two European Cup finals and more than 1,000 competitive matches, Shilton emerged as one of the English game's genuine legends. He has the rare distinction of having played over 100 league games for 5 different clubs.