How does the Bhavanga State relate to the Jhanas?
Jhana is more than just the giving up of the five senses. Each of the jhanas is the result of very strong samadhi, and has specific factors that go along with it. For example, the first jhana has five factors: rapture, pleasure, initial application of mind, sustained application of mind, and oneness of mind. As one goes deeper into the second jhana, one leaves behind initial application and sustained application of mind, and so on.

Bhavanga is very different than this however. Bhavanga is like a blank slate. All it has are the mental factors that are necessary for mind to be there and nothing else. It only occurs in the space between other kinds of mindstate. None of the jhana factors are present at all, and there isn't even any meaningful degree of awareness in it.