Will stock i5 2500 bottleneck gtx 770?

Might depend on what me mean by bottleneck. I submit for proof,

http://www.bit-tech.net/hardware/2013/06/12/intel-core-i5-4670k-haswell-cpu-review/5

Look at the shogun results. Of the "2500K" CPUs, only the 4670K at stock can cross 30FPS. The 3570K crosses on avg, while the 2500k at stock falls shot of 30FPS any way you look at it. I'm sure there are other cases where this will be true. The 2500K at stock will be "behind" other CPUs that are faster. It's still a good performer, but there might be cases out there where you'll want to OC it to get the performance from other chips.
 


Thank you for providing the most irrelevant fps stat. All gamers want 60fps, and the OP wants to know if a 2500k is bottleneck, and this stat shows that even a 4670k falls amazingly short. What's the point of showing how a 4670k can't even keep pace?
 
I believe shogun 2 is an RTS game so 30FPS will do. Which the 2500k stock still can't do. The 4670K is ~30% faster then the 2500k. As I said above, bottleneck might be the wrong word to use. The 2500K won't do as well as the newer chips at stock speeds. Will be "identical" in most cases, but every now and then a game will come along that will cause it to be slower.
 


In non-gaming applications and games at super low resolutions that eliminate the card as a bottleneck? Probably.

Otherwise there's a <5-6 FPS difference at best in most titles at stock speeds. Seriously, the gaming performance difference between Sandy, Ivy and Haswell i5s is so minuscule it's not even funny.