Have agonised over this from first reading. I love the 'Desert Island' nature of the question. I have settled on 3 choices so far:
1. Stonewall Jackson by James Robertson - masterful biography, superb insight, movingly written.
2. Taken at the Flood by Joseph Harsh - ground breaking and demonstrated the way all campaign histories should be written. The first author to acknowledge that McClellan did a pretty good job.
3. The Maryland Campaign of September 1862: Ezra A. Carman’s Definitive Study of the Union and Confederate Armies at Antietam
by Joseph Pierro - brilliant job of putting Ezra Carmen's manuscript into a readable and thoroughly enjoyable form.
I am not too keen side stepping the question by including multivolume works as one. Where do you end? Battles and Leaders volume 1 to 6? Rhea's 'Overland campaign' - 5 volumes? Pfanz's Gettysburg trilogy? David Powell's Chickamauga Campaign - 3 volumes! Surely the question would be if you were limited to only 5 books which ones would you choose? Which volume of Shelby Foote's would you choose because then you have to state which one and why that particular volume?
For example I think I will end up choosing two from:
(a) Rhea's (possibly Cold Harbor - for him making sense of the carnage).
(b) Pfanz's (possibly The Second Day - because this is the most important out of the three).
(c) Decision in the West by Albert Castel - just brilliant and beautifully written.
(d) This Terrible Sound by Peter Cozzens - made an unfathomable battle readable!
(e) Early Photography at Gettysburg by William Frassanito - for doing something no one else had looked at until then!
This is not disrespecting some of the fine authors we have today - Eric Wittenberg, Earl J. Hess, Timothy B. Smith, James Hessler, John Priest, Noah Trudeau, Garry Adelman and numerous others.....
Perhaps that Desert Island does not look so good after all
Brilliant question though...