My laptop's about a year old, but I bought it at quite a high spec then so it's still fine. When I first ran Skyrim, it chose the 'high' graphics setting. At first, the game plays very smoothly, however after a few minutes it starts to slow down, and after about 5 minutes or so the game is unplayable (<5 fps).
Quitting Skyrim completely and reloading it seems to solve the problem, but only for another 5 minutes of play. I've tried turning down the graphics options to their lowest setting, but this doesn't seem to help. Is there a way to diagnose what the problem is, and fix it?