The book You Have the Right to Remain Innocent talks about this for a good portion of it. There are nuances to simply shutting up, invoking the right to remain

The book You Have the Right to Remain Innocent talks about this for a good portion of it. There are nuances to simply shutting up, invoking the right to remain silent (implied by the 5th) and not speaking, invoking the 5th to not answer a question, and invoking the *6th* which is the right to a lawyer. The book agrees that invoking a lawyer is now the correct move since it puts some onus on law enforcement.