Sunday's draw pitched the top four teams in the Premier League against one another, with last season's runners-up City handed a home tie against Jose Mourinho's men.
City came from two goals down to beat Watford 4-2 to book a spot in the last 16, while Chelsea secured a narrow 1-0 victory over Stoke City.
Premier League leaders Arsenal and Liverpool already have a league match scheduled for February 8 and will now meet just a week later in the Cup.
Wigan Athletic head to Cardiff City and the holders' former boss Roberto Martinez will take on another one of his old clubs as Everton host Swansea City.
Nigel Clough's Sheffield United, the lowest-ranked side left in the competition, will take on Nottingham Forest or Preston North End if the League One outfit can get past Fulham in their replay.
Elsewhere, League Cup finalists Sunderland meet Southampton, having beaten them on their way to one Wembley final this term, Brighton and Hove Albion welcome Hull City and Charlton Athletic travel to Hillsborough to tackle Sheffield Wednesday.
Ties will be played on weekend of February 15 and 16.
Full draw for the FA Cup fifth round:
Manchester City v Chelsea
Sheffield United or Fulham v Nottingham Forest or Preston North End
Arsenal v Liverpool
Brighton and Hove Albion v Hull City
Cardiff City v Wigan Athletic
Sheffield Wednesday v Charlton Athletic
Sunderland v Southampton
Everton v Swansea City
