Holders Manchester United will host Fulham at Old Trafford in one of at least three all-Premier League clashes, with League Cup finalists Newcastle United at home to top-tier rivals Brighton & Hove Albion.
Bournemouth will host Wolverhampton Wanderers in another all-top-flight encounter.
Struggling Plymouth caused one of the great upsets of the FA Cup on Sunday when they beat a second-string Liverpool 1-0, ending the Premier League leaders' hopes of a quartet of trophies this season.
The Pilgrims are bottom of the Championship but City, who reached the fifth round with a 2-1 win at third-tier Leyton Orient on Saturday after going behind early on, have been misfiring this season.
There will be a fourth all-Premier League clash if Nottingham Forest avoid trouble at League One (third tier) Exeter City on Tuesday, with Ipswich Town awaiting the winners.
Aston Villa, who ended Tottenham Hotspur's hopes on Sunday, host second-tier Cardiff City.
Crystal Palace, who defeated Doncaster on Monday, will host South London rivals Millwall in a mouthwatering clash.
The fifth-round matches will be played on the weekend of March 1st and 2nd.
Last 16 draw:
Newcastle United vs Brighton & Hove Albion
Bournemouth vs Wolverhampton Wanderers
Manchester City vs Plymouth Argyle
Exeter City or Nottingham Forest vs Ipswich Town