City fought back from a goal down in the fourth round to see off Championship leaders Fulham, while Peterborough beat QPR.
Boreham Wood, the only non-league side left in the competition, will travel to Frank Lampard’s Everton after overcoming Bournemouth.
Draw in full
Luton Town v Chelsea
Crystal Palace v Stoke City
Peterborough United v Manchester City
Liverpool v Norwich City
Southampton v West Ham United
Middlesbrough v Tottenham Hotspur
Nottingham Forest v Huddersfield Town
Everton v Boreham Wood