M.P.
:You don't order a book to replace the one lost. You tell the library it was lost and pay them. I know this from experience. I've lost a couple of books over the years. The probably won't accept another book. The book has to go thru a process within the library and they're not set up for accepting books from patrons.
I also suggest that at 5, the parent holds some responsibility for keeping track of books. I suggest that losing a book is no big deal and not worth punishment. It is a learning experience as you've decided. I'm glad you made that decision.