It will most definitely feel more of a side-grade than a proper upgrade. The i7 3770 is not a slow CPU, even if it is locked.
The i5 9600K is going to be struggling from day 1 with keeping up with everything that's happening thread-wise in a modern PC, just like your i7 3770 may be now. I wouldn't consider anything below a i7 8700K or i7 9700K as an upgrade for it, thinking longer term. Simplifying it a little, going from an i7 to an i5, even with all these years of difference, is going to be a side-grade at worst and a small upgrade at best. Keep also in mind Intel doesn't intend to keep the socket alive for more than 1 or 2 generations, so if you invest in 32GB or RAM, you'll be effectively
locked from upgrading in a couple years to a new CPU or even platform. I'd strongly advice you just spend the shekles on a proper i7 upgrade. And AMD is indeed an option now, so if you're open to suggestions, hang in there until the 7th of July to see how the Ry3K series hold against the Intel lineup.
Also,
@geofelt, Amdahl's law does not apply to systems, but algorithms. A system is composed of a plethora of sub-systems and each sub-system is composed by a plethora of algorithms. Unless your processing is depending on a single algorithm that cannot escale beyond 8 cores due to what-ever, then you'd be correct. For the 99% of stuff running in your PC, it does not apply on a daily basis as they're all independent systems that don't need information sharing. Plus, a PC runs more things than just games at any point in time.
Cheers!