There will be a repeat of last season's FA Cup final after holders Wigan were drawn against Manchester City in the quarter-finals.
Ben Watson's late goal gave Wigan a historic triumph at Wembley in May, and Manuel Pellegrini's City side will be hoping to avenge this defeat when the two clubs meet again at the Etihad on the weekend of March 8/9.
Meanwhile, Everton will travel to face Premier League rivals Arsenal in the sixth round.
The Toffees enjoyed a 3-1 win over Swansea at Goodison Park on Sunday. Goals from Lacina Traore, Leighton Baines and Steven Naismith sealed victory for Roberto Martinez's men.
There was the brief prospect of a Merseyside derby, but Arsenal ended the hopes of Liverpool by beating them 2-1 at the Emirates.
Alex Oxlade-Chamberlain scored in the first half and then set up Lukas Podolski for a second goal soon after the break. Steven Gerrard pulled a goal back from the penalty spot on 59 minutes, but the Gunners held on to gain a measure of revenge for their recent 5-1 humbling at Anfield in the league.
Sunderland boss Gus Poyet could yet be heading back to Brighton after his former employers drew 1-1 with Hull City in Monday night's fifth-round clash at the Amex. They will replay on Monday, 24 February.
Poyet left Brighton in acrimonious circumstances following the club's play-off second-leg defeat against Crystal Palace.
There is also the possibility of a Sheffield derby at Bramall Lane after Wednesday and United were drawn against each other. The League One Blades saw off Nottingham Forest 3-1 on Sunday, while Wednesday's tie with Charlton was postponed due to a waterlogged Hillsborough pitch; that match will now be played on Monday, 24 February.
Arsenal v Everton
Brighton or Hull City v Sunderland
Sheffield United v Sheffield Wednesday or Charlton
Manchester City v Wigan