Taking the fifth is not about truth or falsehood.
It is about not saying a thing.
Listen. If you ever find yourself arrested and being charged with a crime and the police tell you all about your Miranda rights and then seek to question you, the best legal advice is always: shut the **** up. Invoke your right to counsel. Tell them you will invoke the 5th and won’t speak with them until you’ve consulted with counsel — and maybe not after that, either.
Why? Because, otherwise, in order to extricate yourself from the mess you’re then in, you MIGHT say something akin to this. “Look. I saw what happened. I can give you the descriptions of the ones who did it!” Well, guess what? You have just — by your own words — placed yourself at the scene of the crime at the time of the crime.
Speaking can damage your legal position. Even telling the truth can damage your legal position. Even if you’re perfectly innocent.