Gonzalo Higuain netted the first and the fourth, with Cristiano Ronaldo, Luka Modric and Karim Benzema all on target.
The victory keeps Madrid in second place and clear of rivals Atletico, who they will meet in the Copa del Rey.
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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.