...I get a new rig with an i7-5930 CPU, while I have an i7-2600 now?
Only if you take advantage of the support for much faster memory. The i7-2600 has a 3.4 GHz base frequency, max turbo of 3.8; the i7-5930 has a 3.5 GHz base frequency, max turbo of 3.7. This is close enough to identical that you're unlikely to see any difference without careful controlled tests. (The i7-5930 does have more cores, but that doesn't help DF directly.)
However, the i7-2600 has a max memory bandwidth of 21 GB/sec, and is only officially rated for DDR3-1066/1333. The i7-5930 has a max memory bandwidth of 68 GB/sec, and is officially rated for DDR4-1333/1600/2133. If you get DDR4-2133 memory for the new / upgraded system, large forts & worlds *might* run up to three times as fast if the memory bandwidth is the limiting factor on your current system, or up to two times as fast if memory speed is the limiting factor. But there are a lot of complicating factors, and it is even possible that it would not be faster at all, if the limiting factor on your current system is CPU or graphical rendering.
All of the above based on official, rated specs. Getting a motherboard that semi-officially supports DDR4-2400 might improve things further, and mild overclocking might yield even more improvement, *if* memory speed is the limit. (Heavy overclocking tends to result in systems not stable enough for the complex operation of DF.)
My personal suspicion is that on a generally good, modern, system that the memory bandwidth is the limiting factor, at least for larger embarks; DF has to shuffle an enormous amount of data from main memory to the CPU every time tick, far more than CPU caches can handle. Thus I would guess that you would see noticeable improvement going from 21 to 68. But we really have very little idea about how DF breaks down on various systems, and you're talking about spending quite a lot of money for unclear and risky results. I can't honestly recommend it unless this is money you can afford to spend on something fairly risky and ephemeral, or you can justify it on other grounds.
If you *do* upgrade, please try and take some before and after data points about FPS, ideally with identical saved forts and versions. It could provide valuable info on how DF works in the real world; it's rare to see someone upgrading the memory without also a significant increase in clock speed and processor architecture.