Ronaldo, who has reached 230 goals for Los Blancos in the Spanish top flight, was in rampant form having failed to score in Real's opening two league games.
His tally matched the five goals he scored in the 9-1 thrashing of Granada at the back end of last season and on the way the Portuguese superstar notched his 32nd hat-trick for the Madrid giants.
Ronaldo was quickly on the score sheet when he converted from a superb Luka Modric pass and he doubled his tally from the spot after Gareth Bale was felled inside the penalty area.
Bale, in superb form in the more central role he has been playing for the Welsh national side, set up Ronaldo for his third, drawing him level with Raul on 228 La Liga goals.
Former World Player of the Year Ronaldo then turned provider for Karim Benzema to score Real's fourth just before halftime.
Ronado's own fourth, again set up by Bale, took him clear of Raul, who still holds the overall club scoring record, and he added his fifth just before the finish.
"Someone who scores so many goals has their place in history forever like Raul or Di Stefano," said Madrid coach Rafael Benitez after the convincing victory.
"I think we are speaking of three historic players and I hope Cristiano continues adding to his tally for his good and the good of the team."
The match in Barcelona was Real's first since the transfer deadline day when a deal for Manchester United goalkeeper David de Gea collapsed due to a paperwork issue.
It has allowed Keylor Navas to prove he can succeed Iker Casillas and his fine save from Felipe Caicedo did prevent Espanyol from taking an early lead before the goals starting flowing at the other end.
Later, Ronaldo's great rival Lionel Messi proved his immense worth to European and Spanish defending champions Barcelona in a vital 2-1 away win at Atletico Madrid.
Messi started on the bench having missed training on Friday to attend the birth of his second son after returning from international duty with Argentina.
He had to watch as Fernando Torres put the home side ahead in the Calderon, but Neymar leveled for Barca, who dominated much of the match.
But once introduced Messi worked his magic and flicked home the winner 11 minutes from time to leave his side top of the standings, two points clear of Real after three wins from three games.
Home coach Diego Simeone had no doubt as to his influence on the match, despite not playing the full 90 minutes.
"Messi was the difference when he was on the pitch," said Simeone. "He is a player that is used to turning the game and he did it once more today."