Unless there is some sort of underlying medical issue, biting at FIVE is completely INAPPROPRIATE. I applaud you for a real punishment for a something that is a serious issue. He is a little guy, but he can do some serious damage with his mouth and this behavior must end.
I don't think you should give in. Even my THREE year old remembers when I lapse from the usual rules--no matter how I feel in the moment, I always regret it later. Punishments for kids are ALWAYS punishment for the parents too...it is the sacrifice you make. He needs the extra sleep.
Maybe a quick run to the library for a book on tape?
Response to edit: I have a biter too...so I know what you're talking about. Our peditricians would disagree, mine said that she shouldn't be doing it at age three. Period. Guess there really isn't one right answer.