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Karim Benzema, who is battling a knee injury, and Gareth Bale were rested as Real prepare for Tuesday's Champions League game against Wolfsburg.
James Rodriguez steered in a free-kick, with Lucas Vazquez adding a second.
It was 4-0 by half-time, with Ronaldo firing in a square pass from Jese, who tapped in the fourth.
Real trail 2-0 against Wolfsburg as they head into Tuesday's quarter-final second leg at the Bernabeu, with manager Zinedine Zidane acknowledging that his team's season would be over if they fail to progress.
Zidane's side went into the weekend lying seven points behind leaders Barcelona in the title race and with hopes of winning La Liga all but gone.
Eibar, who have failed to win in eight league matches, were caught on the counter-attack repeatedly as they played a high defensive line.
Their performance improved significantly in the second half, though, with midfielder Gonzalo Escalante heading against the bar late on after Borja Baston had glanced on a corner.
Victory on Saturday moved Real up to second place for a couple of hours, although Atletico Madrid regain that position later on Saturday with a 3-1 win at Espanyol.