The Caley Thistle draw was one of just two all Premiership ties with Dundee due to host Celtic in the other one.
Former Wigan Athletic, Bolton Wanderers, Burnley and St Johnstone manager Owen Coyle made the draw alongside Scottish FA vice-president Alan McRae and Eddie Thompson of competition sponsors William Hill.
Full fifth round draw
Queen of the South v St Johnstone
Rangers v Raith Rovers
Dundee v Celtic
Hibs v Arbroath
Falkirk v Annan/Brechin City
Stranraer/Dunfermline v Dundee United
Partick Thistle v St Mirren/Inverness Caley Thistle
Spartans v Berwick Rangers
All Scottish Cup fifth round ties will be played on 7/8 February 2015.