Is my CPU Bottlenecking?

Hey Guys,

I am running at lowest 40fps and at most 80fps on the new black ops (Call of Duty®: Black Ops Cold War) – keeping in note that only 5gbs out of the 8gbs of vram is being used on good settings –  and I have the following specs;

CPU: i5-9600k

GPU: RTX 2070

Ram: 32gb 3200MHz

My friend averages around 80-90 fps on the same settings with the following specs;

CPU: i7-7700

GPU: GTX 1660

Ram: 16gb ??MHz

I suspect a cpu bottleneck, would I correct by thinking that? If so, what can you recommend on replacing the cpu with. 

Thanks for the help, Dr.