I once got a question similar to this, and it seemed like a good post topic. (There were a plague of similar posts floating around the blogosphere awhile back too. I encourage other PCVs with blogs to post their list!) I'm not saying this is the best five books ever written, rather the ones that have influenced me the most.
5) Slaughterhouse-Five, by Kurt Vonnegut. This little sci-fi classic upended my worldview the first time I read it. Vonnegut's views on writing are still some of the most profound that I know. (See here to see what I mean.)
4) Blood Meridian, by Cormac McCarthy. This astonishingly brutal story is written with equally astonishing lyricism. It's also one of the few books that improves with the audiobook version. I highly recommend this version read by Richard Poe.
3) Cadillac Desert, by Marc Reisner. This was the first really good nonfiction book I ever read, and the one that remains dearest to my heart. It was the first unarguable demonstration that even in a successful country like the US, vast sections of policy can have basically no connection to reality or the rational needs of people. Reisner's analysis of the situation is probably more poignant today than it was when it was published in 1986; many of the water crises he predicted are taking place now across the West.
2) War and Peace, by Tolstoy. This is probably the best book I've ever read, or perhaps the best book I understood as a really good book. The only book where I've had to sit back and say just meditate on how damn good the book is. I've read Ulysses, and while I could see how someone might think it was a really good book, I don't have the literary chops to appreciate it. Plus, really introspective books are kind of obnoxious. In War and Peace, the story is as ambitious and epic as its title, and Tolstoy succeeds wildly.
1) Desert Solitaire, by Edward Abbey. This just proves my poor literary taste, apparently. I've loaned this out to several volunteers now, and none have been able to finish so far. But Abbey's caustic wit, his eloquent praise of the desert (my home country) and his trenchant barbs aimed at the very underpinnings of society keep this one fresh for me even after dozens of readings.