It should be fine since those games are not very demanding.
However, I just want to point out one thing... If this was a desktop I would say a 1.6Hz i7 CPU (dual core I suppose) would limit the HD 5870. I would assume that will still be the issue for a laptop. So either drop down to a laptop with a HD 5850 instead to save a little bit of money (and yes the CPU is still slow for this card). Or buy a similar model but with a faster i7 core; which means more $$$.