Pressure was already high on Mikel Arteta after disappointing defeats to Brentford and Chelsea, but a mauling at the Etihad will raise further questions.
The Arsenal defence was carved open with ease as Ilkay Gundogan and Ferran Torres put Pep Guardiola's side two ahead early on.
Granit Xhaka's first half red card made it an insurmountable task as Gabriel Jesus and Rodri both got themselves on the scoresheet to pile on the misery.
City claimed the lead after just seven minutes with Jesus clipping in a superb cross from the right which was powerfully headed in at the back post by Gundogan.
Arsenal goalkeeper Bernd Leno did get his hands to the ball but could not keep it out.
City doubled their advantage five minutes later as Torres was on hand to tuck home after the ball was lobbed into the area by Bernardo Silva.
Things went from bad to worse for Arsenal when Granit Xhaka was sent off after 35 minutes.
Referee Martin Atkinson showed the Switzerland midfielder a straight red card after a reckless two-footed challenge on Joao Cancelo.
Dean Ashton told talkSPORT: "The referees have certainly softened some of the challenges that have gone in, but if you leave the floor with both feet and they're straight out in front of you as you make the challenge, yes he's got the ball but you can't jump in like that.
"When is Granit Xhaka going to learn? It's red card. It's absolutely mindless!"
Jesus made it 3-0 to City just before half-time. Jack Grealish cut into the box and picked out the Brazilian, who took a touch and then slipped the ball past Leno.
Arteta was criticised for his failure to make changes that inevitably led to more goals.
Ashton said: "I'm sorry, but you deserve that Arsenal and Arteta, you haven't made a change since the red card and you've got no midfield, no midfield whatsoever.
"It's so simple. It's three passes and Jesus was licking his lips."
City did not ease up after the break, adding their fourth goal within eight minutes of the restart.
Rodri was the next name to get on the scoresheet, side-footing a shot into the bottom corner from 25 yards with excellent placement.
"It's been so easy for Man City. They've not had to be at their best," Ashton said.
"How long will Arteta last? I've backed him, but after the things I've seen today it's becoming increasingly difficult to back him."
Torres made it 5-0 to City as he glanced in a header off the post from a Riyad Mahrez cross six minutes from time to pile on the misery.
Arsenal are still to score this season and sunk to the bottom of the table.
talkSPORT commentator Nigel Adderley aptly summed up their performance at the end of the game calling it 'a shambles'.