Goals from Nacho Monreal, Mesut Oezil, Alexandre Lacazette, Aaron Ramsey and Alexis Sanchez gave Arsenal their first away win and lifted them up to fifth.
Wayne Rooney and Oumar Niasse scored for Everton, who had Idrissa Gueye sent off in the second half.
The Toffees' fourth league loss in six dropped into the bottom three on goal difference.
Tottenham host Liverpool in Sunday's other game.
Video Goals Arsenal 5-2 Everton
