Just listing a few of my favorite war movies:
The Alamo (2004)
Stalingrad (1993)
Das Boot (1981)
Tunnel Rats (2008)
Full Metal Jacket (1987)
Gettysburg (1993)
Gods and Generals (2003)
Sink the Bismarck! (1960)
Pearl Harbor (2001)
Red Tails (2012)
Flyboys (2006)
U-571 (2000)
In Enemy Hands (2004)
Thirty Seconds over Tokyo (1944)
Fortress (2012)=The one about the B-17 crew not the Sc-Fi one.
Memphis Belle (1990)
Windtalkers (2002)
We Dive at Dawn (1943)
Enemy at the Gates (2001)
Saving Private Ryan (1998)
Zulu (1964)
Act of Valor (2012)
All Quiet on the Western Front (1979)
Glory (1989)
The Red Badge of Courage (1951)
Gallipoli (1981)

In no particular order, mine are:

Saving Private Ryan
All Quiet on the Western Front
Glory
The Longest Day
Three Kings

All Quiet is 1930 I believe...

There are some interesting picks for a 16 year old.  I'm surprised you've seen Zulu, Full Metal Jacket, Thirty Seconds over Tokyo, and some of the older movies.  That's some serious war movie watching.

I have no particular order but I like 

Operation Petticoat
The Thin Red Line
Full Metal Jacket
Jarhead
Zulu
The Hurt Locker

I was in the Marines for six years so watching Full Metal Jacket and Jarhead made me laugh.  I thought, "Yeah, that's pretty close."  They did a great job with portraying the military and life and all.

Lastly, Pearl Harbor isn't a war movie.  It's terrible from the standpoint of a war movie.  It's a romance with some bombs thrown in there.  I hated that movie and it was a massive waste of time for me.  They downplayed the importance of Doolittle's raid and it was all Kate Beckinsale, or whoever, and she's fine to look at but she doesn't belong in a war movie.

5)Saving Private Ryan
4)Red Dawn (2012)
3)The 9th Company
2)Platoon
1)Grave Of The Fireflies(anime, but it is based off of the Pacific missions in WW2, so I'm guessing it still counts.)

Wow this is a toughie 

1. The Longest Day
2. The Alamo (john Wayne) I think it would qualify as a war movie cause it highlights Texas's war for independence from Mexico 
3. The Dirty Dozen 
4. MaCale's navy Joins the air force
5. Midway 
 

I'm not very good at picking what movies I like over the other ones, I either like it or I don't, but here are 5 of some of my favorites...

Stalingrad
Downfall(great to see the fall of Berlin from a different perspective)
Saving Private Ryan(of course)
Full Metal Jacket
Schindler's list(just an amazing movie

Of course there are dozens of others that I like too.

I forgot about Downfall which also reminded me of Valkyrie which I also really liked.

My whole list is wrong!! D:

My favorite 5, not necessarily in order, but Full Metal Jacket is definitely the list topper.

Full Metal Jacket
Jar Head
Saving Private Ryan
Windtalkers
We Were Soldiers

All of these are amazing movies, and Full Metal Jacket is actually known as one of the most accurate portrayals of old school Marine Boot Camp, not quite what is was, but one of the closest movie portrayals there is. Amazing movie. I also really like Red Dawn, and The Hurt Locker.

Stalingrad,
Forrest Gump, 
The ninth company, 
The cranes are flying.
All great movies if you ask me

In no particular order, here are my favorite War movies:

1. Star Wars Episode IV: A New Hope
2. Star Wars Episode V: The Empire Strikes Back
3. Star Wars Episode VI: Return of the Jedi
4. Star Wars Episode I: The Phantom Menace
5. Star Wars Episode III: I forgot the name.

... Oh hey, they're all Star Wars... I also like Forrest Gump.

This may not be a 'war' movie per se (at least not between two interplanetary civilizations, that is), but it is about a war between the human race and aliens. Independence Day. I love it!

I'm not too into war, so I'd say the two closest (since I couldn't think of five) would be Avengers and Captain America...oh, and Thor would work, too, I think...I doubt this is what you meant, but I'm standing by Captain America as my favorite.

In no particular order
Forrest Bump
Saving Private Ryan
Valkyrie
Schindlers List (no doubt the best movie on this list)
And a toss up between Platoon or Stalingrad.

I'm a huge fan of War history especially World War 2 and the Vietnam War. So these movies are perfect.

Lord of the rings

Full metal Jacket

King Arthur

Star Wars

Kingdom of Heaven

Not sure you count these movies as War movie. But in every of those is some kind of war going on.

My five favorite war movies would have to be (not any specific order)

Act of Valor
Inglorious Bastards
The Hurt Locker (I love Jeremy Renner)
Machine Gun Preacher (Don't know if this counts)
Brothers (I really don't like Toby Maguire and this movie didn't change that. But I really love Timothy Olyphant)
The Expendables 2 (Love the actors and the movie was just so funny)

OK that was six.

I don't really have 5 favorite war movies.. I would say that 2 of my favorites are the alamo and saving private ryan if I had to put a couple of more on that list I would say, Full Metal Jacket, Three kings and The longest day, they were pretty good!

warmaker : "There are some interesting picks for a 16 year old.  I'm surprised
you've seen Zulu, Full Metal Jacket, Thirty Seconds over Tokyo, and some
of the older movies.  That's some serious war movie watching."

Ha! I'm that rare 16 year old who does not care about Black Ops 2 and instead plays The History Channel's Civil War!

My all time favorite war movie is Horatio Hornblower. Its a movie about a 17 year old boarding on of the English boats later getting promoted to captain.