Hmmm, seeing as that my car takes a little while to start up, is starting to worry me.

It'll crank for awhile and then start up. But after I run it for about 5-10 minutes I can go and park it, and try to start it, and it will start fine, but then it'll die after 5-10 seconds of it being started. And then another 15 seconds later, I tried to start it, it starts but dies. Then another 15 seconds later, I start it up with no problems.

What is the problem? I just recently put in an alternator and battery...

 

Well, you can always take it to a Autozone and they can hook it up to a car diagnostic machine and maybe find a faulty part. Does it chug before it dies?

 

Doesn't chug at all, just dies. Looks like I'll be going to autozone. =/

 

What are all the noises you hear when you try to start it and it doesn't? Do you hear clicking or belts turning?

Here are some possible problems for the stalling:

Idle speed icorrect,
Fuel filter clogged,
distributer components damp or damaged,
faulty/incorrectly gapped spark plugs,
faulty sparks plug wires,
vaccum leak in fuel injection system, intake manifold, or vaccum hoses
valve clearances incorrectly set

Starting problems:

leaking fuel injectors
faulty fuel pump
pressure regulator
ignition components damp or damaged
corroded battery terminals, especially the ground
air filter clogged

Being that you say the car doesn't chug when it dies, I don't think it's a problem with fuel. Normally the car will chug/surge when that is a issue becaues the car gets a little but not enough gas and responds accordingly.