It's easy to get that idea from watching cop shows, so I don't blame you for thinking so, but it's not actually true. Once you invoke your Fifth Amendment righ

It's easy to get that idea from watching cop shows, so I don't blame you for thinking so, but it's not actually true. Once you invoke your Fifth Amendment rights, as simply as saying "I want to talk to a lawyer", interrogation must stop until your attorney is present. That means stop asking questions, period. Cops are typically pretty mindful of this— since after that, any questions they ask, and anything you say in response, is inadmissible, and in fact could go to poison whatever legitimate case they have outside your testimony. You do still have to watch out; this doesn't apply to "offered statements" which aren't in response to direct interrogation ("You know, Jim, there's a lot of kids around here. It'd be a shame if one of them found that shotgun...") At that point they may be able to claim you voluntarily waived your right to remain silent and resume questioning. (It's also worth noting that the Fifth Amendment only applies once you're under arrest. It's a protection from self-incrimination, after all.