Harold Bloom's Shakespeare: The Invention of the Human continues to provide interesting analysis. I also recently looked at Asimov's Guide to Shakespeare, primarily because Asimov is a long-time favorite writer of mine. I quite like it, but unfortunately I don't have a copy. I'll be sure to pick one up from the library so I can look at everything he has to say about Henry V.
I also found a book on my shelf which I didn't even remember having. It's called A Natural Perspective: The Development of Shakespearean Comedy and Romance, and it is by Northrop Frye. I'm going to be sure to check that out at some point, and I'll post here when I do.