Hi, there. I have similar graphic cards configuration: 5650 and 4250. But this is a HP dv6 3160us... and has no BIOS switching option.
I tried almost everything... and I'm tired, really tired and no time to go on trying things.
I never could use 5650 discrete card, NEVER. When trying, only black boot screen (or some boot text, too). Only once, I could boot on that card, using vgaswitcheroo... but it was slower than 4250 with proprietary drivers (I need 3D acceleration).
The driver that works OK with 4250 is 12.4, on Ubuntu 12.04. Older drivers had artifacts, newer's don't support 4250... but neither the 5650.
Does anybody know something about this laptop?