All five goals came in a frantic first half, Gonzalo Higuain opening the scoring before Cristiano Ronaldo and Angel di Maria scored braces.
Real are still seven points behind city rivals Atletico and 15 behind Barcelona.
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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.