John Wile’s hard-working, but limited, Fourth Division side of 1985-86 battled through four rounds before losing 1-0 to a Dean Saunders goal in a fifth round replay at Second Division Brighton.
That Posh team finished 17th in Division Four.
Posh also reached the fifth round in the 1964-65, 1974-75 and 1980-81 seasons. The 1964-65 team reached the quarter-finals where they lost to Chelsea at Stamford Bridge, a feat never repeated.
Peterborough United should make a couple of changes to their starting line-up for the visit of Sheffield Wednesday
Posh chairman Darragh MacAnthony: 'Put the hard yards in or we'll get beaten'
Peterborough United manager Grant McCann explains why it’s difficult finding a replacement for Sammie Szmodics.
Poku is too important to be risked by Peterborough United, plus injury updates on Butler, Norburn and Fernandez
Peterborough United talking points: 'The diminishing value of Ronnie Edwards, a manager more impressed by hard work and performance than reputation and Bali Mumba's behaviour'
The 1974-75 Posh team lost 2-0 at Middlesbrough in a fifth round replay and the 1980-81 side were beaten 1-0 at home by Manchester City in their fifth round game.