Neil Warnock's men knocked out Spurs 2-1 at Elland Road to book a trip to the Etihad Stadium in the pick of the ties.
Non-league Luton, who claimed a famous 1-0 win at Norwich on Saturday, missed out on a plum draw with a top Premier League side as they got Millwall at home.
Oldham, the npower League One side who stunned Liverpool 3-2 on Sunday, were handed their Merseyside rivals Everton at home in the next round.
Manchester United were drawn to face Reading at Old Trafford, while Arsenal also got a home tie, against Championship outfit Blackburn.
Chelsea, should they see off Brentford in a replay after the two sides drew 2-2 at Griffin Park on Sunday, can look forward to a trip to Middlesbrough.
QPR's conquerors MK Dons were drawn at home to Barnsley, while Wigan will travel to Huddersfield or Leicester.
The ties will be played on the weekend of February 16.
FA Cup Fifth Round Fixtures
Huddersfield/Leicester vs Wigan
MK Dons vs Barnsley
Oldham vs Everton
Luton vs Millwall
Arsenal vs Blackburn
Man City vs Leeds
Man Utd vs Reading
Middlesbrough vs Brentford/Chelsea