Let me save you some trouble here... you already ran out of lives before you declared that you wanted to use the book of death, so the book of death would be ineffective. (The book's function is to stop the loss of any further lives after activation; the best time to declare its activation is before you begin combat on a stage.)

So here's what will happen: your stage 5 is over. You get your book of death back for stage 6 (as if you had never activated it). Stage 6 is the last opportunity to use items, so you should declare that you're activating the book of death first -- before you do anything else on stage 6.