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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.