The Potters caused the upset of the round with their victory over Arsenal yesterday and now must make the trip to Eastlands over the weekend of 13/14 February.
Holders Chelsea will be confident of making the last eight after being drawn at home to Championship side Cardiff City, while Fulham take on the winners of Notts County v Wigan.
Aston Villa travel to either Crystal Palace or Wolves, but perhaps the most exciting tie of the round pits Southampton with fierce south-coast rivals Portsmouth at St Mary’s.
At least one Championship side will be in the quarter-final draw after Reading were paired with West Brom.
FA CUP | FIFTH ROUND DRAW
Wolves or Crystal Palace v Aston Villa
Manchester City v Stoke City
Derby County v Birmingham City
Bolton v Tottenham or Leeds
Chelsea v Cardiff City
Fulham v Notts County or Wigan
Reading v West Brom
Southampton v Portsmouth