I haven't looked inside the pc, but it must be a 500w because I am running the gtx660 currently
Model H77H2-EM
CPU Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz
16gb Ram
2 x SSD
500W PSUs greatly vary in quality. The exact brand and model is, in many cases,
the most important specs of a PC to know, as it is here. If we could only choose
one bit of information about your PC to answer a GPU upgrade question, it would almost always be the information about the PSU.
Now, a GTX 1050 uses very little power and can be recommended generally safely on all but the most horrifying 500W PSUs (which, again, is why we need to know). But other GPU recommendations, it can be a different matter.
In all honestly, I'd just stay with with I have right now if you can. The GTX 1050 is an upgrade, but not a huge one, and the GPU market is such a godawful mess that you'll pay more for a used 1050 than you did for a new one back when it was new. The whole semiconductor + supply lines + tariffs + crypto mess means that buying a GPU is basically an exercise in "spending too much."