CPU help and advice

[Equitorium]

Hi,
So I've currently got a gtx 1080 on an msi Intel Z270 motherboard. My current CPU is an i5 (not sure what and cant check right now), but it bottlenecks a lot of the higher end games I play e.g. siege runs at around 50fps and lag spikes a lot. I was looking to upgrade to a better cpu, something like an i5-9600k but wasn't sure if that was the best thing to go for/if it's compatible? My budget is around £300.
Any help would be appreciated.
Thanks

 

[Equitorium]

I'm currently playing at 1080 on a 144hz monitor, I'm not looking to upgrade my mobo any time soon as I recent bought the last one, probably should've got z390 at the time lol.

 

[Equitorium]

Thank you for all the replies.
Say I wanted to upgrade today, I've noticed my ram is only 2400mhz. I've had a look on Amazon and found the b450 for £90, the ryzen 2700 for £200 or the 2700x for £260 and 16gb 3000mhz ram for £65. Would all of that work/be okay? Or would I need anything else or any changes that'd be better? Thanks