Madrid moved ahead in the match seven minutes before the break when Angel di Maria produced a cool finish from close range and it was three after 44 minutes when Ronaldo headed his second of the match.
Madrid continued to threaten in the second period and they added gloss to the scoreline when Pepe scored a header and Ronaldo completed his hat-trick from the spot late on.
Here, Sports Mole dissects the 90 minutes of action between the two La Liga rivals.
On target 13
On target 2
Was the result fair?
Without question. Deportivo took the lead with their first effort of the match and in truth they could have entered the break more than two goals behind. Madrid were wasteful at times in the opening period, but they always looked capable of scoring in each attack. The fact that 5-1 does not flatter Madrid tells you everything that you need to know.
Real Madrid's performance
7/10. Madrid started the match slowly at home – as they so often do – but they matured into the latter stages of the half. Di Maria began to cause havoc as Madrid moved 3-1 ahead and all but wrapped up the three points before the second period. Meanwhile, Ronaldo took his tally to six league goals with a hat-trick.
4/10. Deportivo certainly gave their maximum this evening, but they were just miles behind their opponents. Their season will not be based on how many points they pick up against Madrid & Co, rather those around them. They fought to the very end, however, which will stand them in good stead this season.
Sports Mole's man of the match
Angel di Maria: The Argentine has had his critics since joining the club, myself included, but he was just brilliant this evening. He won the first-half penalty for his side, as well as adding a fine goal of his own. On this form, he is just unplayable.
Biggest gaffe of the match
Manuel Pablo recklessly dived in on Di Maria in the opening half, handing Madrid the chance to level the score from the spot. It was all one-way traffic from there.
Miguel Angel Ayza Gamez had a fairly straightforward 90 minutes of action this evening. He rightly awarded Madrid two penalties and largely remained unnoticed, which is always a good sign for a referee.
Real Madrid: Jose Mourinho's side travel to Ajax in the Champions League on Wednesday before facing Barcelona in La Liga next Sunday.
Deportivo: Deportivo will attempt to return to winning ways when they face Rayo Vallecano in the league next Saturday.