Sutton, who reached the last-16 after beating Leeds 1-0, will now host Arsenal at Gander Green Lane.
Fellow non-league side Lincoln City are away to Premier League Burnley.
Holders Manchester United will go to Blackburn Rovers, while Premier League leaders Chelsea also travel to a Championship club after drawing Wolves
The eight fifth-round ties are due to be played between Friday, 17 February and Monday, 20 February.
Two non-league teams are in the draw for the FA Cup fifth round
Fifth Round Draw:
Burnley v Lincoln
Fulham v Tottenham
Blackburn v Manchester United
Sutton v Arsenal
Manchester United's FA Cup player ratings against Wigan
Sun, January 29, 2017
Express Sport brings you Manchester United's player ratings from their FA Cup fourth round win over Wigan Athletic
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Sergio Romero – 7.1
Middlesbrough v Oxford
Wolves v Chelsea
Huddersfield v Manchester City
Millwall v Derby or Leicester