. After like 5 minutes or so, it will tell me basically that Minecraft has run out of memory and it will give me the option too either quit the game or go back to the main menu. But, my computer is brand new and definitely has enough memory.

Put the summary of the bug you're having here

What I expected to happen was...:
Describe what you thought should happen here

What actually happened was...:
Describe what happened here

Steps to Reproduce:
1. Open the game, and log in.
2. ...Play for about 5 minutes
3. ... and it crashes