Help choosing CPU for AMD Radeon RX 6750 XT

Hi guys.

I’ve bought Amd Radeon Rx 6750 XT as my new GPU. Im witnessing stutters, fps drops etc, and my other specs are old. (Cpu intel core i5-6500)

I dont have a big budget, so does anyone have budget-friendly CPU’s best for this GPU? Ive read old posts but those are pretty old.

And do I have to upgrade my Mobo at the same time? (MSI B150M Mortar)

Many thanks in advance, im very noob with these stuff.