The Hammers crushed Doncaster Rovers 4-0 and will now travel to Old Trafford in the next round, after United beat Liverpool 3-2 in Sunday’s clash.
Wolves were the first side that qualified for the fifth round, beating Chorley 1-0 and will host Southampton, who ended Arsenal’s defence with a 1-0 win.
Manchester City will face Swansea and Barnsley take on Chelsea.
Everton could face Tottenham if both Premier League teams can see off Sheffield Wednesday and Wycombe respectively.
See the complete FA Cup fifth-round fixtures below:
Leicester vs Brighton
Swansea vs Man City
Everton vs Wycombe/Tottenham
Barnsley vs Chelsea
Wolves vs Southampton
Sheff Utd vs Bristol City
Man Utd vs West Ham
Burnley vs Bournemouth/Crawley
Wednesday, February 10 has been scheduled for FA Cup Fifth round to be played.