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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.