United knocked Rangers out of last season's tournament, days before the Ibrox oldco club went into administration.
Celtic face a trip to Raith Rovers, the team that shocked them in the 1994-95 League Cup final, should they get past Arbroath in a fourth-round replay.
Scottish Cup fifth round draw:
Raith Rovers v Celtic or Arbroath
St Mirren v Cowdenbeath or St Johnstone
Dunfermline v Dumbarton or Hamilton
Hibernian v Aberdeen
Falkirk v Forfar
Dundee Utd v Rangers
Dundee v Turriff United or Morton
Kilmarnock v Inverness
Ties to be played weekend of February 2 and 3