Under the 5th you have the right to remain sikent to avoid self incrimination. But you have to remain completely silent. And if you do say anything, you'd better be sure it's true. Lying to the police or in a court is a felony although you'd never know it considering how police routinely commit perjury in courtrooms and seldom get so much as a slap on the wrist for doing it.
As any defense attorney will tell you: Fon't talk to the police. Period. Don't affirm, deny, or argue with them. Stand mute except to politely and calmly keep repeating you don't consent to any questioning without your attorney present nor (and this is extremely important) do you consent to any searches.
Don't speak if you've done something.
And especially don't speak if you haven't done anything.
Sad it's reached this point. But as any lawyer will tell you: Don't talk to the police. Don't consent to any searches.