The Gunners headed into the game looking to return to winning ways after the disappointment of their 2-1 loss to Watford last time out.
Wayne Rooney gave the home side the lead in the 12th minute but Nacho Monreal equalised for the visitors before half-time.
Goals from Mesut Ozil, Alexandre Lacazette, Aaron Ramsey and Alexis Sanchez in the second half completed the rout for the Gunners as they returned to winning ways in style.
And Arsenal legend Henry was impressed by what he saw from the Gunners at Goodison Park.
Speaking on Sky Sports after the game, Henry said: “It was very good.
“Right from the start, obviously they conceded a goal early, but right from the start you could sense they were going to mean business today.
“If you’re looking from an Everton point of view, that’s exactly how you don’t play Arsenal.
“If you give them time on the ball and allow them to play like they played today, you’re in trouble.
“They scored five, it could have been five each half in all fairness.”
Arsenal’s win left them in fifth place in the Premier League table and level on points with Chelsea.
The north London side are nine points behind leaders Manchester City in the race for the Premier League title, however.
The Gunners return to Premier League action next weekend when they take on Swansea City at The Emirates next weekend.
The Gunners have not won the title since their famous unbeaten triumph in the 2003-04 campaign.
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