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HD5870. Now Im not able to use RX 480 in 10.12.4 so I'm not sure about that one.

The stock Apple HD5870? Did you check if the cable and monitor are normal?

It only happen in 10.12.4?

If you boot to recovery partition, everything is normal?

This fault can be reproduce every single time? Happen straight away boot? Or suddenly happen in random manner?
 
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