The Owls, who beat Hereford 4-1 on Saturday, are through to the last 16 for the first time this century.
Wednesday today strengthened their squad ahead of the remainder of the season with the signature of midfielder Isaiah Osbourne, 23, from Aston Villa to the end of the season.
Non-league Crawley Town knocked Torquay United out yesterday and accounted for Championship side Derby in the third round.
They have been rewarded with a trip to Manchester United in the fifth round.
Arsenal, who today knocked out Huddersfield Town, will travel to Leyton Orient.
FA Cup fifth round draw
West Ham v Burnley
Notts County/Manchester City v Aston Villa
Stoke v Brighton
Birmingham v Sheffield Wednesday
Leyton Orient v Arsenal
Everton/Chelsea v Reading
Manchester United v Crawley
Fulham/Tottenham v Bolton/Wigan
Matches to be played on the weekend of February 19-20.