League One Stevenage have been drawn against Tottenham in the FA Cup fifth round as a reward for reaching the last 16 for the first time.
Brighton will meet Liverpool at Anfield after beating Premier League Newcastle in the previous round.
Chelsea host Birmingham, with League Two Crawley Town handed a tough home game against Stoke.
Norwich take on Leicester, while Everton welcome Blackpool or Sheffield Wednesday to Goodison Park.
Bolton will fancy their chances of making the sixth round as they travel to Millwall or Southampton.
Sunderland boss Martin O'Neill could face former club Aston Villa if the Black Cats win their replay against Middlesbrough and Villa beat Arsenal on Sunday.
But O'Neill played down that prospect after his side drew 1-1 with their north-east rivals on Sunday.
"That's a long way away," he said. "We have a really difficult game against Middlesbrough and I would not think too much about [facing Aston Villa]."
Crawley Town beat Hull City 1-0 in round four on Saturday and their chief executive Alan Williams said: "This is the first time we have faced Premier League opposition at the Broadfield Stadium in a competitive fixture and I'm sure the ground will be packed.
"It's another wonderful occasion for the club, the players and the fans and we look forward to welcoming Tony Pulis and his side here next month."
Brighton gave Kenny Dalglish's Liverpool a scare before losing 2-1 in the Carling Cup in September, but the Seagulls have not been beaten in three FA Cup visits to Anfield.
The fifth-round games will be played on the weekend of 18-19 February.
FA Cup fifth round
Liverpool v Brighton
Everton v Blackpool or Sheffield Wednesday
Chelsea v Birmingham
Crawley Town v Stoke
Stevenage v Tottenham
Norwich v Leicester
Sunderland or Middlesbrough v Arsenal or Aston Villa
Millwall or Southampton v Bolton