United knocked Rangers out of last season's tournament, days before the Ibrox oldco club went into administration.
Celtic face a trip to Rovers, the team that shocked them in the 1994-95 League Cup final, should they get past Arbroath in a fourth-round replay.
Hibernian's reward for their derby win over holders Hearts is another home tie against SPL opposition in the form of Aberdeen or Motherwell, who drew 1-1 at Pittodrie on Saturday.
Another top-flight tie will see Kilmarnock host the winners of the Highland derby replay between Inverness and Ross County.
St Mirren are at home again following their win over Brechin, facing the winners of tomorrow night's rearranged clash between Cowdenbeath and St Johnstone.
Dundee are at home against Turriff United or Morton. The Highland League side held Allan Moore's team to a 1-1 home draw on Saturday.
Dunfermline are at home to the winners of the postponed clash between Dumbarton and Hamilton, while Falkirk will host Forfar.
The ties will be played on the weekend of February 2 and 3 next year.
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 or Motherwell
Falkirk v Forfar
Dundee Utd v Rangers
Dundee v Turriff United or Morton
Kilmarnock v Ross County or Inverness
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