what's the model of the laptop? I'm assuming since you have a 1st gen i5 and a 5470M its either a 7741G or 5741G. Most of those, BUT NOT ALL OF THOSE, had an available 5650M GPU w/ 1GB of VRAM option, so if you can find a MOTHERBOARD for your model with THAT upgraded chipset, it might work... but it would cost probably $200 (US) to do everything...
See my video, I upgraded my 7741 with Intel HD graphics to a motherboard with your 5470M:
http/www.youtube.com/watch?v=QwwzqsiJMTE
Honestly, for as much effort and money, its really not worth it. While the 5650M is a decent mid range GPU chipset, its starting to get a little aged.
If you are willing to attempt the upgrade, make sure the seller has a picture of the ACTUAL motherboard and you can see 4 VRAM chips on it and not the 2 memory chips like your 5470M 512MB motherboard has before buying it...
For $500 you can get a BRAND NEW laptop with a better 6550M or something like that out of a DV6 HP.
Also if you are interested, check out my video of adding an external GPU to the same 7741.
http/www.youtube.com/watch?v=ktUw2VTFyX4
Still, these types of upgrades typically aren't worth the time and hassle, especially since your laptop is pushing 3 generations old.
Happy hunting!
Dry