The pair will now face off at Ibrox on the weekend of February 5 and 6.
The other seven fixtures will be confirmed after fourth round replays are played on January 18.
Other fifth round fixtures
Aberdeen v Montrose or Dunfermline Athletic
East Stirlingshire or Buckie Thistle v Brechin City
Hamilton Academical v Dundee United or Ross County
Hibernian or Ayr United v St Mirren or Peterhead
Inverness CT v Morton or Airdrie United
Stenhousemuir or Threave Rovers or Stranraer v Motherwell
St Johnstone v Falkirk or Partick Thistle