City came from behind to beat Fulham 4-1 while Chelsea defeated Plymouth Argyle 2-1 in extra time on Saturday.
Tottenham Hotspur, who saw off Brighton & Hove Albion 3-1, must travel to Middlesbrough, who beat Manchester United on penalties at Old Trafford.
In an all-Premier League clash, Southampton host West Ham United who survived a potential upset at the hands of non-league side Kidderminster Harriers with last-gasp goals in normal time and extra time.
The winners of Sunday’s game between Liverpool and Cardiff City will host Norwich City while defending champions Leicester City must first see off Nottingham Forest, with the winners hosting Huddersfield Town.
The fifth-round games will be played in the week commencing Feb. 28.
FA CUP FIFTH ROUND DRAW
Luton Town v Chelsea
Crystal Palace vs Stoke City
Peterborough United v Manchester City
Liverpool/Cardiff City v Norwich City
Southampton v West Ham United
Middlesbrough v Tottenham Hotspur
Nottingham Forest/Leicester City v Huddersfield Town
Everton v Bournemouth/Boreham Wood