It was complete domination from the off for Pep Guardiola's side, with chances for David Silva and Sergio Aguero. The tie was over by the end of the first period, with goals from Yaya Toure,Silva and a own goal from Havard Nordtveit.
Their dominance carried over into second period, with Aguero adding the fourth five minutes after the restart. The game went quiet after that point before John Stones added a fifth to round off a comfortable victory.
The London Stadium was the stage to kickstart the third round of he world's most historic cup competition, and it was set to be a good clash with both sides starting brightly.
It was City who looked to draw the first blow, with slick passing opening the Hammers defence to allow Silva through on goal. The Spaniard's effort looked good but his compatriot Adrian did well to get down low and block his near post effort with his feet.
The hosts reacted almost instantly as Antonio tried one from the edge of the area, but his deflected was well cleared by Willy Caballero.
Adrian was called upon once again in the 27th minute, and the Spaniard produced an excellent save to keep the scoreline goalless. A corner fell to the feet of Aguero 10 yards out, the Argentine's effort looked good but Adrian went one better to tip his effort over the crossbar.
Slaven Bilic's side looked strong as the first period neared it's end, however their cup journey came to an end in a blistering 12 minutes from the visitors.
The perfect opportunity arrived in the 33rd minute as a slick move was ended with Pablo Zabaleta been clipped in the area by Angelo Ogbonna, which forced Michael Oliver to point to the spot. Toure stood up and though Adrian went the right way, he could do nothing to keep out the Ivorian's fourth goal of the season.
The Hammers should have been back in it almost instantaneously, when Antonio's blinding run and effort was parried by Caballero. It fell to the feet of Sofiane Feghouli with the goal gaping but the returning winger managed to put it wide.
A double blow was handed at the end of the half, and a blunder from a Hammer was what seemed to kill off the home side. It was another slick move from City in the 41st minute as Bacary Sagna swung the ball into the box, it look intended for Raheem Sterling to turn home but Nordtveit beat him to it as he put it beyond Adrian.
It was a masterclass from Guardiola's side, as they added a third just before the break. It was once again slick movement from City as Sterling broke into area before playing it Siva, his first touch caught Adrian off guard and it was simple enough to tap it home.
Wrapping it up
Bilic will have given a stern talking to his side as they headed out for the second period, but all plans will have been thrown out as City added a fourth in the 50th minute.
It was quite a fluke considering the quality that City had been producing, Sterling showed great skill before teeing it up for Toure and his drive at goal was deflected home by Aguero.
City's fifth and final goal of their thrashing was added six minutes from time. Mark Noble will have thought he did enough to block Stones' header on the line after Nolito's corner, but Oliver's watch judged differently and sealed West Ham's whimpering exit from the FA Cup.