The great Blues opened the scoring through Gabriel Jesus in the first half and turned on the style in the second, inspired by an excellent Kevin De Bruyne, with further goals from Bernardo, De Bruyne, an own goal and a late Sergio Aguero penalty.
City played better in the second half and with the win advance.
On to the reaction:
Pep Guardiola Reaction
“I am really pleased for the commitment,” he stated. “Especially with all the games in our legs and minds.
“Of course, we have to improve a few things but we made good movements and I’m satisfied to be in the next round and the draw on Monday.”
On City’s record-breaking recent goal gluts, Guardiola added: “I think all the clubs – everyone – play to score goals.
“Everyone wants to win and that’s why. We do it for the people but we have done it from the beginning, since we arrived here.
“Winning eight games in a row, this month has been good. I could say it’s because we played against lower league sides but it’s what we have to do.
“Everybody has played and we want to arrive in the last stages of the FA Cup and Champions League, and fight to the end in the Premier League and Carabao Cup. It’s the only way I understand.
“What these guys have done in the past 16 months is incredible. We will see wat happens in the next few games to see if we can catch Liverpool.
“We analyse game by game and everybody is ready.”
“It’s not easy when players have long injuries,” he said. “That’s why we tried to handle his minutes.
“Of course, we need him because he’s so clever and aggressive in his game. He helps a lot.”
Asked if he would relish or fear the prospect of a Manchester Derby in the FA Cup Fifth Round draw, Guardiola replied: “I can’t control the draw!
“It’s important to be in there. United have also won eight games in a row but I don’t know what the draw will be.
“Hopefully, we can go through.”
Gran victoria en nuestra casa! Estamos en la próxima ronda!! #ManchesterCity 5-0 #Burnley #FACup— Nicolas Otamendi (@Notamendi30) January 26, 2019
Great home win! We’re on to the next round! #ManchesterCity 5-0 #Burnley #FACup pic.twitter.com/4f92YnnipN
See you next week for Premier League action v Newcastle! Come on City!