Well.... I guess I'll give it a shot.
First off, are you saying that the disc stops exactly @ the 5-10 minute mark on the disc or are you saying that after about 5-10 minutes (regardless of what part of the disc you are playing) that it shuts down. If it's the former, I would assume something could be obstructing the laser's movement. If it's the latter, this could be heat related in respect to a cold solder joint having developed on one of the boards or other electrical part of the player.
Regardless, you should open up the player and make an observation of what you may or may not see (especially pay attention when the player does it's abrupt stop). Also, test it with a CD and see if it does the same thing as well. Report back when you have some new information to share about the problem.