This could be caused by an out of date graphics driver, or possibly a faulty graphics card.
The HD5xxx series has reached peak optimisation and been moved to legacy status, there will not be any further driver updates for your product. More information available here.
The latest Crimson driver for your system is 16.2.1 and is available here.
The last Catalyst driver for your system is 15.11.1 Beta and is available here.
I would recommend using DDU to sweep your system of AMD drivers, and then trying one or both of drivers above to see if they resolve your issue with the black screen while gaming.
I followed your steps, and I genuinely say thank you. I've been looking for a solution for 7 months and I finally I find one that works. Again, thank you!
Glad to hear it.