PanHandler.......Grant finally finished proofing his work on July 14, 1885. He died on July 23, 1885. If your book was "signed" on May 23 of 1885, it a forgery because he was still writing the book at that time. You got taken by whoever sold or gave you that book. He never live long enough to see his book published. So as first edition goes, it might be worth something but the signature is a forgery pure and simple. If you don't believe me.....looked it up:
Grant's Last Battle: The Story Behind the Personal Memoirs of Ulysses S. Grant (Emerging Civil War Series) Paperback  – July 19, 2015  ,  This is an excellent book, you can get it off Amazon like I did.