While third-tier side Stevenage will host eight-time champion Tottenham in the last 16, Crawley of League Two will host last season's beaten finalist on the weekend of Feb. 18-19.
Crawley beat League Championship clubs Hull and Bristol City in the last two rounds.
"This is the first time we have hosted Premier League opposition at the Broadfield Stadium in a competitive fixture and I'm sure the ground will be packed," Crawley chief executive Alan Williams said. "It's another wonderful occasion for the club, the players and the fans."
Liverpool's reward for a 2-1 fourth-round win over traditional rival Manchester United is another home match, this time against a Brighton side that knocked out Premier League club Newcastle on Saturday.
Chelsea will host Birmingham, Norwich will host Leicester, and Bolton will go to the winner of the replay between Millwall and Southampton.
Everton will host Blackpool or Sheffield Wednesday, while the winner of Sunday's late game between Arsenal and Aston Villa will play Sunderland or Middlesbrough. Sunderland and Boro drew 1-1 Sunday and will replay Feb. 7.