The Cumbrian part-timers, one of only two League 1 clubs still in the competition, are coached by former Bradford, St Helens and Great Britain stand-off Leon Pryce.
Pryce said: ''It's an absolutely fantastic draw for the club. It will be a great day out for all of Workington. This is why the Challenge Cup is so special."
The tie at Headingley will pit Leeds prop Brad Singleton against his younger brother Perry, a centre or second-rower with Workington.
The four Super League clubs entering at the fifth-round stage were all kept apart, with Hull KR, London Broncos and Salford paired with Championship opponents in Leigh, Halifax and Rochdale respectively.
Halifax beat London 26-16 at the Shay in the Championship 12 months ago and Broncos coach Danny Ward is expecting another difficult trip into West Yorkshire.
"It's going to be a tough game but one we look forward to," said Ward, whose side have defied expectations by winning three of their first seven games in Super League.
St Helens-based Thatto Heath, the only amateur club in the competition after knocking out League 1 North Wales Crusaders in the fourth round, were rewarded with a home tie against Dewsbury.
The draw, made at Wembley by former Wigan winger Martin Offiah and Linzi Prescott, widow of former St Helens and Hull full-back Steve Prescott, paired Bradford and Featherstone in a repeat of the 1973 final which Bradford won 33-14 at Wembley.
The eight winners will be joined by the top eight from last season's Super League, including the 2018 Challenge Cup winners Catalans Dragons, in the sixth-round draw on Monday, April 15.
Challenge Cup fifth-round ties (to be played on the weekend of April 13-14): Hull KR v Leigh, Widnes v York, Thatto Heath v Dewsbury, Leeds v Workington, Halifax v London Broncos, Bradford v Featherstone, Salford v Rochdale, Doncaster v Batley.
