http://www.theacerguy.com/2008/12/morris-aspire-5920-gpu-swapupgrade/
This is a link to a gentleman who swapped his gpu on his Aspire 5920, from an 8600 to a 3650 because he said there were issues with the 8600. Apparently, you're not the only one, ha. Since you had an 8600 in it, it has the MXM (Mobile PCI Express Module) in it, so you will be able to replace it. Obviously, an 8600 would be no problem, A type 2 would work and it would be easier if it had the Acer bios flashed to it, like he said. I myself have replaced a few mxm gpu's, but I've always been careful to check the compatibility beforehand. Make sure its the right type, as a wrong one will simply not work and the chassis probably only allows space for the original type anyway. I searched for type 2 cards and the only ones I could find were 8600's and below. Ebay has a few type 2's up for sale. There is an 8800 gtx, but its a type 3. Keep looking and you might find one more powerful in a type 2 format. Also this site:
http://www.mxm-upgrade.com/types.html lets you know about the different type's and it even has an upgrade section for your laptop. Good luck!
P.S. - Also keep in mind the power requirements. If its the same or less powerful gpu, you *shouldn't* have a problem. However, if it's a more powerful one, even if the mainboard accomodates it, that doesn't necessarily mean your power supply can handle it. There are a lot of things to consider.