The holders will take on the 12-time winners at Stamford Bridge next month.
Holders Chelsea have been drawn to face Manchester United in the FA Cup fifth round in a repeat of last year’s final.
In the stand out tie of the round, Maurizio Sarri’s side will take on Ole Gunnar Solskjær’s improving Red Devils at Stamford Bridge next month.
Eden Hazard scored the only goal when the sides met at Wembley in May, with Chelsea lifting the trophy for the eighth time.
Elsewhere in the draw, League Two Newport could face Premier League champions Manchester City if they beat Middlesbrough in their fourth round replay.
League One Doncaster, through to the fifth round for the first time in 63 years, will host Crystal Palace.
AFC Wimbledon, who beat West Ham in round four, have been drawn to face Everton’s conquerors Millwall.
Bristol City will face either Shrewsbury or Wolves, who needed a stoppage-time to secure a replay against the League One side on Saturday.
Watford also face an away trip in round five, against either League One Portsmouth or Championship QPR.
Derby, who needed a late goal so squeeze past Accrington in round four, face a trip to Brighton or West Brom in the last 16.
Swansea will play either Barnet or Brentford, who face each other at the Hive on Monday evening.
The FA Cup fifth round ties will take place the weekend of 15-18 February.
FA Cup fifth round draw in full:
Bristol City v Shrewsbury Town or Wolverhampton Wanderers
AFC Wimbledon v Millwall
Doncaster Rovers v Crystal Palace
Middlesbrough or Newport County v Manchester City
Chelsea v Manchester United
Swansea v Barnet or Brentford
Brighton or West Brom or Derby County