Chelsea, who beat Everton 2-1 in last year's FA Cup final at Wembley, eased past Championship outfit Preston 2-0 in the fourth round with goals from Nicolas Anelka and Daniel Sturridge.
Carlo Ancelotti's side currently occupy third place in the Premier League and are in the hunt for three major trophies this season, with the first leg of their Champions League last-16 tie against Inter Milan also taking place in February.
Cardiff, who were beaten 1-0 by Portsmouth in the 2008 FA Cup final, overcame Leicester 4-2 in the previous round.
Stoke were rewarded for their win over Arsenal by being handed another tough draw against Manchester City.
Tony Pulis' side pulled off a shock by beating Arsene Wenger's side 3-1 at the Britannia Stadium on Sunday, while Roberto Mancini's Manchester City side overpowered Scunthorpe.
After knocking out Manchester United, Leeds will once again face Premier League opposition if they win their replay with Tottenham after they were drawn against Owen Coyle's Bolton at the Reebok Stadium.
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