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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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.