I think that quotes should be used for clarity. As Edwin Ashworth has described, italics could also work as a matter of opinion if that option were allowed to you.
As the purpose of your sentence is to educate those unfamiliar with the idiom, it might not be as clear that they couldn't "use the fifth" or other less idiomatic constructs. It could be unclear whether "taking" is part of the phrase.
Consider : Business travelers will sometimes avoid losing a day to travel by traveling from California to New York on a flight boarding late evening California Time(commonly referred to as taking 'the red-eye' ).
In that case, it is really "the red-eye" that is the common slang ... "taking" could be replaced with "booking the red-eye" or "flying on the red-eye", "caught the red-eye" etc.