Living with a Core i5-8600
This processor sits in the lower part of the range and will be the limiting component in most modern pairings. Frame rates will be capped by the chip well before the graphics card runs out of capacity, and no graphics upgrade will change that.
If frame rates are the problem, this is where the money goes. Raising the resolution will not help here in the way it does for a graphics-limited system.
A small cache holds this chip back
9 MB of L3 is modest by current standards, and it costs this chip more in games than its clock speed suggests. Game engines walk large, scattered data structures, so a small cache means more trips to main memory and more stalls on the render thread. Memory speed and timings matter unusually much on a part like this.
A note on age
Released in 2018, this chip is 8 years old. Beyond raw speed it is on an older platform, which usually means slower memory, fewer PCIe lanes and no path to a newer processor without replacing the motherboard. Factor that into any upgrade maths — the chip may not be the only thing you end up replacing.
Where it sits
Ranked 179 of 201 desktop processors for gaming. Nearest faster: Core i3-10325, Core i3-10320. Just below: Core i5-8600K, Core i3-10305. Full method on the methodology page.