Now that's a tough fucking question TM. I'm a big war film buff, and the choices are endless. Do I go with an epic like Saving Private Ryan? Do I go with a film dealing with the mental effects of war, like Apocalypse Now? Or do I go the unconventional route and go with a war film from a different perspective other than that of America, like Letters From Iwo Jima, Gallipoli, or Das Boot?
All of the films I just named are dear to my heart. I'll try my best to come up with a list of five films TM, but I know I'll be leaving something vital out. The five films that come to mind though are Platoon, Apocalypse Now, The Thin Red Line, Saving Private Ryan, and Gallipoli.
Vietnam war films tend to be my favorite, probably because of the effect it had on my parents generation and the closeness and fascination I've always felt with the 1960s. When it comes to Vienam films, there are two that take the cake, and those are Platoon and Apocalypse Now. While I believe Apocalypse Now is the better overall film of the two, Platoon is the better war film if that makes sense. Apocalypse Now deals with much more than just the conflict in Vietnam, whereas Platoon is just the daily life of a soldier in the war and all of the lows and highs. Several scenes in that film never fail to disturb me, particularly those involving the psychotic Bunny (Kevin Dillon of Entourage fame).
When it comes down to it, I'd go with either Platoon, or the criminally overlooked Thin Red Line. Sucks that Saving Private Ryan overshadowed this film, because frankly I think it's twice the film Ryan is without a bit of the sentimentalism. Countless great performances, brutal and expertly staged battles on Guadalcanal, a true epic in every sense of the word. If you've never seen it, I HIGHLY recommend you get your hands on it immediately.
Honorable mentions to Full Metal Jacket, Deer Hunter, Paths of Glory, The Longest Day, Letters From Iwo Jima, and Black Hawk Down.
Oh...and, uh, did you really pick Enemy At the Gates TM? That film was terrible from start to finish.