Boreham Wood, the lowest-ranked side left in the competition, will face Frank Lampard's Everton after they overcame Championship side Bournemouth.
Nottingham Forest's reward for eliminating holders Leicester City in their Midlands derby is a home tie against Huddersfield Town.
Crystal Palace, managed by four-time FA Cup-winner Patrick Vieira, welcome Stoke City.
Ties will be played on Wednesday March 5 to minimise disruption to league fixtures.
FA Cup fifth-round draw
Luton Town vs. Chelsea
Crystal Palace vs. Stoke City
Peterborough United vs. Manchester City
Liverpool vs. Norwich City
Southampton vs. West Ham United
Middlesbrough vs. Tottenham Hotspur
Nottingham Forest vs. Huddersfield Town
Everton vs. AFC Boreham Wood