[I didn’t see user6726’s excellent answer until after I finished mine. There’s quite a bit overlap — except that he discusses immunity, which I ignore — but I think there’s enough difference that some readers may benefit from seeing both.]
TL;DNR: No, you could not “take the 5th” to avoid embarrassment. If you tried and got caught, you’d get in trouble. As for your speeding ticket hypothetical: I’ll take the 5th!
To answer this question, it will help to be clear on what it means to take the 5th. Contrary to popular belief, taking the 5th is not about admitting guilt. Taking the 5th is about avoiding legal trouble caused by one’s testimony. As Justice Clark said in 1951, in Hoffman v. US, a witness can only take the 5th if she “has reasonable cause to apprehend danger” from answering the question.
(This explains why an innocent person can take the 5th. Since some innocent people look guilty, and some innocent people are found guilty, some innocent people might reasonably fear that testifying will get them convicted. To avoid that danger, they, too, can take the 5th.)
As you point out, witnesses might face a variety of non-legal dangers if they testify, such as embarrassment. Or they might be confused about the legal dangers they face. What keeps these witnesses from “falsely” taking the 5th?
The answer is simple. As Justice Clark said in Hoffman,
“The witness is not exonerated from answering merely because he declares that, in so doing he would incriminate himself — his say-so does not of itself establish the hazard of incrimination. It is for the court to say whether his silence is justified, and to require him to answer if it ‘clearly appears to the court that he is mistaken.’”
Figuring out whether a witness really will be in danger if she incriminates herself raises some tricky problems. To convince the judge, the witness may have to actually incriminate herself. To prevent this, the judge will talk to the witness in private. If the judge finds the witness is not in danger, he will order her to testify. If she does not, the judge can put her in jail, or fine her, for contempt-of-court.
To see the problem judges face, consider why I took the 5th on the speeder question. My hunch is that the speeder cannot take the 5th. It seems to me that the danger she faces is too “small” compared to the damage caused by not hearing her testimony. But I am not sure; I worry that I might be wrong. To avoid embarrassing myself by showing my ignorance, I took the 5th to avoid answering the question. Here’s the catch: By explaining why I need to take the 5th, I end up incriminating myself, in which case, I don’t need to take the 5th!
