That's tough. On the one hand it's an i7, so on the multiple threaded games you'd actually catch a break and should get decent performance from 8 threads. On the other hand, day-z and pubg are both strong in single thread performance, which is where that i7 is going to suffer, both from lack of instruction sets, age of process size and speed of the cpu. 2.8GHz with a much smaller IPC than modern cpus is going to hurt.
The hd5850 isn't doing you any favors either.
With lga1156, you really have no upgrade options, you already have an i7 on a H board, so even OC is out. It's a pre-built, so your bios is castrated, there's only a few cpus that are even recognised, because of the limited cpu power available, a larger gpu is going to...