The HD 5850 falls in line with the newer R7-260X. Your processor is in line with the faster Phenom II X4s. I would say that the gfx card could be improved on for better performance. One thing though... that computer is listed as coming with an A10-6700, not a 6700K.
http://h10025.www1.hp.com/ewfrf/wc/document?docname=c03933886&cc=us&dlc=en&lc=en
Can you verify that it is indeed a 6700K? IF so, it can be easily OC'd for improved performance. But I have not heard of a 6700K. Run CPU-Z and it will ID the processor.
http://www.cpuid.com/softwares/cpu-z.html
If you feel the need to upgrade the processor, the motherboard, the PSU, case.. you may as well build a new gaming PC.
According to the link above, that PC came with an OEM 300W PSU. How you are managing to run a 151W HD 5850 is beyond me. I'm surprised the system doesn't shut down when the card becomes loaded heavily during gaming. I don't expect the PSU to last much longer if you game much.