Nuno Espírito Santo’s side are currently fourth favourites with the bookmakers to lift the iconic trophy. But they have seen their chances boosted further after avoiding a potential clash with Premier League big-hitters Manchester City, Manchester United or Chelsea.
The Molineux men enjoyed a memorable win on the way to the Championship title at Ashton Gate last season when Ryan Bennett headed an injury-time winner to see off Lee Johnson’s side.
If Wolves do beat Salop and the Robins, they are likely to enter the quarter-finals as third favourites to win the competition after holders Chelsea were drawn against Manchester United.
Albion will host Derby County if they win their replay against Brighton. Winners of fifth round matches receive £360,000 in prize money.
Full draw: Bristol City v Wolves or Shrewsbury; AFC Wimbledon v Millwall; Doncaster Rovers v Crystal Palace; Middlesbrough or Newport County v Man City; Chelsea v Man United; Swansea v Barnet or Brentford; Portsmouth or QPR v Watford; Brighton or Albion v Derby.