Rangers will have to take on SPL opponents in Dundee United at Tannadice, while Celtic - if they can win their fourth round replay at Arbroath - will have to travel again to meet Raith Rovers.
United knocked Rangers out of last season's tournament, days before the Ibrox oldco club went into administration. Raith Rovers shocked Celtic in the 1994-95 League Cup final.
Two fifth round ties grouped three SPL sides in each: Hibernian against the winners of Aberdeen/Motherwell's replay, while Kilmarnock will host Highland opposition in the shape of either Ross County or Inverness Caledonian Thistle.
Hibernian beat current cup holders Hearts to qualify for the fifth round and drew 1-1 against Motherwell at Pittodrie on Saturday.
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 draw in full:
Dundee v Turriff United/Morton
Dundee United v Rangers
Dunfermline v Dumbarton/Hamilton
Falkirk v Forfar
Hibernian v Aberdeen/Motherwell
Kilmarnock v Ross County/Inverness Caledonian Thistle
Raith Rovers v Celtic/Arbroath
St Mirren v Cowdenbeath/St Johnstone
Games are to be played on the weekend of February 2/3 next year.