The fourth round clash was postponed on Saturday due to a waterlogged pitch.
Awaiting the winners will be the winner of Kettering Town or Leamington, who also play on Tuesday night.
Both clubs play in the National League North, alongside the Daniels’ fourth round opponents.
Stamford are the sole Northern Premier League representative left in the competition.
FA Trophy fifth round draw
Sutton United v Bromley or Woking
Aldershot Town v Solihull Moors v Boston United or Chesterfield
Darlington v Wealdstone or Gloucester City
Stamford or Hereford v Kettering Town or Leamington
Havant & Waterlooville v Notts County
FC Halifax Town or Southport v Boreham Wood or Torquay United
Oxford City v Peterborough Sports
Hornchurch v Maidstone United
Games to be played on Saturday 6 February. Winning club to receive £6,000 and losing club to receive £1,750.