The possible opponents meet tonight at Spotland, kick-off 8pm.
The draw, which was shown live on The One Show, ensures that a former Rover will return to Ewood Park.
League One Dale are managed by Keith Hill, who made over 100 appearances for Rovers between 1987-1992, while Premier League side Stoke City are managed by former Rovers player and manager Mark Hughes.
The Welshman made 50 league appearances for Rovers, lifting the Worthington Cup in Cardiff in February 2002. He returned to Ewood Park as manager in September 2004, twice taking Rovers to the semi-finals of the FA Cup.
Rovers booked their place in the fifth round of the competition courtesy of an impressive 3-1 victory over Premier League outfit Swansea City at Ewood Park on Saturday.
Rochdale, who are currently fifth in League One, knocked out Northampton Town (2-1) and Aldershot Town (4-1) after replays, before beating Championship side Nottingham Forest 1-0 in round three.
Stoke, who sit 10th in the Premier League, were 3-1 winners at home to Wrexham in the last round.
Rovers drew 1-1 with Stoke City in a pre-season friendly at Ewood Park back in August and 2-2 at Spotland in a pre-season friendly 12 months earlier.
Fifth round draw in full:
Crystal Palace vs. Liverpool or Bolton Wanderers
Arsenal vs. Middlesbrough
Aston Villa vs. Leicester City
West Bromwich Albion vs. West Ham United
Bradford City vs. Sunderland or Fulham
Blackburn Rovers vs. Rochdale or Stoke City
Derby County vs. Reading
Preston North End or Sheffield United vs. Cambridge United or Manchester United.
Ties will be played over the weekend of February 14th/15th.