The highlight of the draw sees a mouth-watering tie at Stamford Bridge
Tottenham, West Ham, Everton and Newcastle were among a host of Premier League big guns to be dumped out in the fourth round over the weekend.
AFC Wimbledon and Millwall claimed memorable cup upsets while Newport and Shrewsbury are still in the competition after securing replays against Middlesbrough and Wolves.
Chelsea, who won the historic tournament last season, beat Sheffield Wednesday yesterday while both Manchester giants are still going for glory this term.
The Blues will now take on United, who beat Arsenal on Friday, at Stamford Bridge in the fifth round.
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Manchester City will take on Middlesbrough or Newport, while Wimbledon and Millwall will go head-to-head at The Cherry Red Records Stadium.
Swansea are set to face the winner of Barnet vs Brentford and Brighton or West Brom will entertain Derby.
The fifth-round ties will take place between 15-18 February.
FA Cup fifth round draw in full
Bristol City vs Shrewsbury or Wolves
AFC Wimbledon vs Millwall
Doncaster vs Crystal Palace
Middlesbrough or Newport vs Manchester City
Chelsea vs Manchester United
Swansea vs Barnet or Brentford
Portsmouth or QPR vs Watford
Brighton or West Brom vs Derby