Benzema added the fifth in injury time in a game played in Kiev.
The French international striker goes on trial in France on Wednesday with four other men accused of complicity in the attempted blackmail of his former international teammate Mathieu Valbuena in a case known as the "sextape affair".
It is not known if Benzema will be present for the start of the trial.
It was a welcome win for Real Madrid, the 13-time European champions, after they slipped to an embarrassing home defeat to Moldovan minnows Sheriff Tiraspol in their last match.
Sheriff lost 3-1 to Inter Milan on Tuesday but Madrid are still second to them in Group D with both clubs on six points.