Several people who commented on my post mentioned books about food-gathering or ship-building. I don't understand this. No, I didn't explicitly rule out such books, but to choose them suggests that the person didn't grasp the import of the question. It's not a puzzle. I'm not asking you to solve a dilemma. I'm trying to find out what you enjoy reading. Even though I didn't say it, you should have been able to figure out that there will be ample food and creature comforts on the island. Also, there is no way off. Those facts are implicit in the question.
This is related to something I mentioned the other day. There is a difference between solving a problem and evading a problem. Suppose my toaster stops working and I ask for your assistance in repairing it. If you tell me to buy a new toaster, you have done nothing to solve my problem. You are evading my problem, and therefore doing me no good. When philosophers describe fact situations and ask questions about them, you are to take the facts as given. Don't fight the facts! If I present a situation in which you have two choices, A and B, and ask which you would choose and why, you are evading my question if you search for a third choice, C.
Again: You are going to spend the rest of your life on an island, alone. Your needs are provided for. You can have five books. What are they, and why? (By the way, some of you mentioned sets of books. No. Five books. If you want five volumes of an encyclopedia, fine; but you can't have the entire set plus four other books.)