It's not about "the i7 series". It's about what GENERATION of i7, or i5, or i3, or whatever. Each generation generally sees some kind of improvement.
It might be a bump in clock speed, which gives you faster single core performance and therefore more performance for ALL cores.
It might be the improvement of IPC, or "instructions per clock/cycle". Which is this:
https://en.wikipedia.org/wiki/Instructions_per_cycle
Or it might be the addition of more cores or hyperthreads, which improve multithreaded performance.
In this case, it isn't just the increase in clock speed that makes a difference. Going from your Sandy bridge i5 to an Ivy bridge i7, IF your motherboard supports it, and just because the sockets are the same does not always mean it will although many motherboards DO support the Ivy bridge CPUs if the originally came with Sandy bridge parts but a BIOS update will usually be necessary, could offer a significant bump in performance because not only are you gaining clock speed and IPC, but also the addition of four hyperthreads.
This is what you'd be looking at, roughly, in terms of gains.
https://www.cpubenchmark.net/compare/Intel-i5-2500-vs-Intel-i7-3770K/803vs2
That's approximately a 49% increase in performance. Now, that won't be all the time, because some of that is due to the addition of the four hyperthreads and there are some games and applications that are not optimized to take advantage of many cores, but you would still likely see about a 10-15% increase in single core performance if the game or application, or whatever process is involved, is only capable of utilizing four cores or less.
So depending on what kind of price you can get that CPU for, it could be well worth it, especially considering that these days the vast majority of software IS well optimized for multithreaded performance.