Leeds United will travel to either Fulham or Sunderland after their 1-1 draw on Saturday, while Tottenham will play either non-league Wrexham or Sheffield United.
Brighton's reward for beating Liverpool is a trip to Championship strugglers Stoke City.
At least one football league team will be in the quarter-finals after Ipswich or Burnley were drawn against Sheffield Wednesday or Fleetwood Town.
The ties will be played from Wednesday March 1st.
FA Cup fifth round draw:
Southampton v Luton Town or Grimsby Town
Leicester City v Blackburn Rovers or Birmingham City
Stoke City v Brighton
Wrexham or Sheffield United v Tottenham
Fulham or Sunderland v Leeds United
Bristol City v Manchester City
Manchester United v West Ham
Ipswich Town or Burnley v Sheffield Wednesday or Fleetwood Town
