The other all-Prem matchups in the next round will feature Wolverhampton Wanderers vs. Southampton, Leicester City vs. Brighton, and Tottenham Hotspur vs. Everton. Southampton eliminated defending champions Arsenal on Saturday to keep their cup hopes alive.
The final two ties are yet to be determined. And Burnley await Bournemouth who beat Crawley on Tuesday.
The fifth-round matches will be played the week beginning Feb. 8.
Fifth round: Week beginning Feb. 8
Burnley vs. Bournemouth
Man United vs. West Ham
Sheff United vs. Bristol City
Wolves vs. Southampton
Barnsley vs. Chelsea
Swansea vs. Manchester City
Leicester City vs. Brighton
Everton vs. Tottenham