Hard to say without a reference board to look at (I'm pretty sure this is actually an HD 5500). Are there any marks on the piece? It's hard to see as the picture's kinda blurry. You'll be hard-pressed to find documentation of this nature.
If it's technically working, I'd just leave the GPU in. I wouldn't worry about not being able to overclock; the fps gains are likely negligible.
How old is the new PC? If it has integrated graphics, basically any integrated graphics over the last eight years or so ought to be outperforming this GPU.
In any case, it's probably not worth the effort to solder. You should only solder if you're willing to buy a new GPU and if you're willing to buy a new GPU, you can get used ones that are faster than this in the $20 range on eBay.