I'd say if you are aiming for 60fps game experience on 1080p even in newer titles paired with something like RX 570,580 or GTX 960,970,1050,1060.
You will be perfectly OK assuming you have 8GB of Ram (at least).
Fortnite will be ok, in fact fortnite can run on toaster (if you lower details and resolution enough) but don't expect Lara's latest SoTR to be super great detailed experience. But you will be ok playing Apex, Division 2, Anthem with reasonable playable frames. Just don't over spend on upgrading the graphic card. Also as mentioned above it is rather expensive heater (power consumption) so if you pair that with a graphic card just make sure your PSU can take that.
Oh and to answer your question, its good for gaming, yes (good enough). Great? no (heat, power consuption, old , slow ddr3 memory) interestingly enough it seems that your graphic card might actually be actually the bottleneck for you system
Bottleneck calculation for Intel Xeon X5680 and AMD Radeon RX 560 with screen resolution of 1920 × 1080 pixels for General Tasks.
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