Probably time to ask what your whole system specs are.
-PSU brand and exact model?
-What storage does the system have?
-What is the CPU cooler?
-What RAM is it using? (2x4gb 1333mhz ?)
-Windows version and is it with the latest updates installed?
-Which particular brand/model R9390X,
-What case is it all in?
Does it only crash with Witcher 3 and Assassins Creed Unity? Can you play any other games ok, and does it ever crash on desktop? Can you run a CPU stress test like Prime 95 blend test for 15 minutes without errors or crashes? What are your GPU and CPU temperature under stress?
Can all be useful for someone to know when troubleshooting.
I don't think you have driver problems due to them being old, they stopped supporting your card in June and the games you are talking about are way older then that.
Did you do a full clean install of the GPU drivers? Sometimes just installing over the top doesn't work properly and its an easy thing to do to be sure.
As
@DXCHASE said white block type artifacts sounds like it could be a VRAM problem, in which case we can't help you I'm afraid, you'd need to borrow another video card and test it to see for sure. Similarly if its a PSU issue, the only way to know for sure is to try another one.
One easy thing to do is to pull out the card and make sure its seated properly and all power cables are properly attached at both ends. If there's a second PCI-e slot its worth giving it a try too and testing.
Few things there, have a look and see. Maybe someone else will have more ideas as well
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