Kenny Dalglish's side, who are already through to the League Cup final in which they face Cardiff City, beat Manchester United 2-1 on Saturday in the fourth round and will be fancied to get past Gus Poyet's Brighton side.
Brighton, who reached the final in 1983 before falling on hard times, knocked out Premier League Newcastle United in the biggest upset of the fourth round.
Chelsea will host Birmingham City while Arsenal or Aston Villa travel to either Middlesbrough or Sunderland.
Crawley Town, who are enjoying their first season in the Football League, fly the flag for League Two (fourth division) with a plum tie against last year's runners-up Stoke City.
Another David versus Goliath clash on the weekend of February 18-19 is Stevenage's home tie with Premier League title contenders Tottenham Hotspur.
English FA Cup fifth round draw made on Sunday: (numerals denote division, Premier League unless stated).
Liverpool v Brighton & Hove Albion (II) Everton v Blackpool (II)/Sheffield Wednesday (III) Chelsea v Birmingham City (II) Crawley Town (IV) v Stoke City Stevenage (III) v Tottenham Hotspur Norwich City v Leicester City (II) Sunderland/Middlesbrough (II) v Arsenal/Aston Villa Millwall (II)/Southampton (II)v Bolton Wanderers
* Ties to be played over the weekend of February 18