The top four sides in the Premier League will fight it out against each other in two mouthwatering clashes.
"No problem - if you want to be the best, you have to play the best," said Chelsea manager Mourinho after the draw, which puts them into a match away at a Manchester City who have not lost at home all season in domestic competitions.
"It'll be a great experience for us. It'll be a big game."
Arsenal's draw throws up an extraordinary sequence of matches for the Gunners: in the space of 11 days from February 8, they will face Liverpool and Manchester United in the league, then Liverpool in the FA Cup, and three days later Bayern Munich in the Champions League.
Everton boss Roberto Martinez will take on his former club Swansea in another stand-out fixture, while Sheffield Wednesday were drawn against Charlton to ensure that at least one non-Premier League side will make it to the quarter-finals.
Matches will be played on 15th and 16th Februrary.
FA Cup Fifth Round Draw
Manchester City v Chelsea
Arsenal v Liverpool
Brighton & Hove Albion v Hull City
Cardiff City v Wigan Athletic
Everton v Swansea City