Jose Reyes put Sevilla ahead early on and it was 4-0 at half time thanks to another goal from the ex Arsenal man, and two from Fabrizio Fazio.
Real Betis were then forced to play with 10 men after a red card but Ruben Castro pulled one back, before Sevilla scored a fifth through Ivan Rakitic.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.