Ticket and travel details for the game will be confirmed in the coming days.
Thomas Frank's side set up a meeting with The Swans after easing past Barnet 3-1 in tonight's Fourth Round replay, Sergi Canos, Julian Jeanvier, and Neal Maupay on the scoresheet.
The Swans also saw off lower-league opposition in the Fourth Round, beating League One Gillingham 4-1 at The Liberty Stadium.
The fixture in South Wales marks our furthest run in the FA Cup since 2006 while The Swans have now reached the Last 16 of the FA Cup in consecutive seasons for the first time since 1964-65.
The full Fifth Round draw is as follows:
Bristol City v Wolverhampton Wanderers
AFC Wimbledon v Millwall
Doncaster Rovers v Crystal Palace
Newport County v Manchester City
Chelsea v Manchester United
Swansea v Brentford
Queens Park Rangers v Watford
Brighton & Hove Albion or West Bromwich Albion v Derby County
From this season onwards, Fifth Round ties will be played to a finish on the day, with extra-time and penalties if necessary.