Gaming-wise , you might see a 5-15 FPS increase by going from the A8-5500 to the A10-5800K.
The thing is: the PSU in your system is a 300W one unless you upgraded it to a more powerful, aftermarket one.
The A8-5500 is a 65W APU while the A10-5800K is a 100W chip. The difference in wattage itself wouldn't be an issue if we had a beefier PSU in that system, but with 300W to spare...a nearly 40W difference might cause trouble. I don't know what other hardware you have in your PC, whether it's all stock hardware or you added anything else.
Given the PC doesn't come with a dedicated GPU and that it only uses 1 HDD....you might be able to upgrade to the A10-5800K without problems given you'd most likely have a total power consumption of less than 300W, even with a 100W CPU. (CPUs, GPUs and HDDs are usually the main power hogs).