Championship outfit Reading have a tough trip awaiting them, having been drawn against either holders Chelsea or Everton, while Burnley travel to Upton Park to face West Ham United.
The only all-Premier-League fixture sees Fulham host Bolton, who won a fourth-round replay at Wigan 1-0.
Steve Evans, boss of Blue Square Premier side Crawley, was understandably delighted to land a money-spinning tie against United, who have won the FA Cup a record 11 times.
"It was just a surreal moment," said Evans, whose side followed victory over Derby with a 1-0 triumph over Torquay.
"I suppose if you are Arsene Wenger or Alec McLeish you don't want that draw - but we did.
"We will approach the tie in a really positive nature.
"The only non-league club capable of beating Manchester United is Crawley Town as we stand today. Miracles do happen."
Leyton Orient chairman Barry Hearn was another happy man, after his League One side were given a home draw against Arsenal.
"We're in danger of breaking even - I don't know what's happening these days with football," he joked.
"But the money is secondary. I've been chairman for nearly 16 years and we've never had anything like this. It's going to be a fabulous day out. I love the FA Cup."
The matches, excepting the Everton/Chelsea v Reading fixture, are due to be played over the weekend of 19-20 February.
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