A home tie against Sheffield Wednesday or Fleetwood awaits the winners of Town's fourth round FA Cup replay at Burnley.
The Owls and Cod Army, who signed former Blues striker Jack Marriott from Peterborough today, drew 1-1 at Hillsborough on Saturday.
Wednesday are second in League One, four points ahead of Town with a game in hand, while Fleetwood are 17th.
They will meet again in a replay at the Highbury Stadium in just over a week's time with Town similarly travelling to Turf Moor to take on the Clarets.
The Blues' only FA Cup meeting with the Owls was at the fifth round stage in 1985 when Town won 3-2 at Portman Road when George Burley, Romeo Zondervan and Alan Sunderland were the scorers.
Town, who were last in the fifth round in 2007, have never faced Fleetwood in the competition.
Fifth round matches will played in the midweek commencing Monday 27th February.
FA Cup Fifth Round
1 Southampton v Luton Town or Grimsby Town
2 Leicester City v Blackburn Rovers or Birmingham City
3 Stoke City v Brighton & Hove Albion
4 Wrexham or Sheffield United v Tottenham Hotspur
5 Fulham or Sunderland v Leeds United
6 Bristol City v Manchester City
7 Manchester United v Derby County or West Ham United
8 Ipswich Town or Burnley v Sheffield Wednesday or Fleetwood