I would like to work with you on this issue as I was one of the original owners of the 390x shortly after it released back in June. I stumbled upon this dx11 issue when I swapped out my PowerColor PCS+ R9 290x for an MSI R9 390x for FFXIV: Heavensward DX11. I do not have GTA V so I cannot comment on that however, from my own testing and observation the broader issue here appears to be related to DX11 titles + the 390/390x + any of the current 15.x drivers that support the R9 300 series cards.
I have already duplicated the issue on 3 different MSI 390x cards on 15.15, 15.20, 15.7, 15.7.1, with the only exception being 15.8 beta (I didn't test the latest beta). I tested on 3 different desktop computers, one with Win 8.1 x64, one with Win 7 x64, and another Win 7 x64. The difference between the 2 Win7 computers is that one is intel i7 based, the other is AMD FX8350 based.
Power supply is not an issue as these computers have XFX XXX Core Edition 850W single Rail or Corsair RM850 series psus. Also, when I revert to the 290x there are no issues. When I install a gtx 970, there are also no issues.
GTA V isn't a very good title to be trying to troubleshoot as that game is notorious for stability issues across both GPU vendors. I strongly believe that if we can fix the dx11 crash issues on the freely available FFXIV: Heavensward benchmark, we'll solve most of the major concerns.
Again, here is the video that demonstrates the major problem here that most users are complaining about.
Here is the link to the benchmark if you want to test it yourself.
I currently do not have the 390x card anymore (haven't for over a month) but I will consider repurchasing it from my local Microcenter if you want to pursue investigating this issue further.