upgrade i5 to i7 processor
what are compatible i7 processors for the 2013 27" i5 imacs?
First I think you're not going to gain enough given the costs and the risks in opening this system.
I would strongly recommend you review the IFIXIT teardown for this model: iMac Intel 27" EMC 2639 Teardown. IFIXIT gave it a 5 out of 10 on repairability.
Here is the IFIXIT guide on removing the logic board which you must do to swap out the CPU: iMac Intel 27" EMC 2639 Logic Board Replacement Note their warning here Potentially Dangerous You will need to review the Teardown Step 5 on pulling the CPU.
Here is a good reference tool to see the performance differences between the systems: Ultimate Mac Comparison Chart. You will need to select the different models you want to compare.
Now one does need to look at the Geekbench performance numbers very carefully here as what the system can do in these tests does not reflect in the real world! Most Apps are not programed to leverage Hyper-Threading so you will only gain the raw performance of the i5 not the i7 numbers of the same design & clock speed. Basically you get very little benefit upgrading the current CPUs.
I would strongly recommend you sell your system and get a new one Vs trying to upgrade it, it will cost less if you really need this level of performance and I would jump to a Mac Pro Vs an iMac (which is what we are doing) as you will have much more head room to grow.
As to the CPU's here is the breakdown for this system:
22 nm, 64-bit "Fourth Generation" Intel Core i5/i7 "Haswell" processor LGA 1155 (Socket H2)
Core i5 3.2GHz (I5-4570)
Core i5 3.4GHz (I5-4670)
Core i7 3.5GHz (I7-4771)
Don´t know the entire list of compatible ones, but I replaced the i5-4570 for an i7-4771 and it worked fine.
I tried with the i7-4790 as well but that one wasn't compatible.
This would be extremely risky and I do not recommend doing so. One suggestion I have is getting a decent PC from Dell, HP, Asus, etc. that comes with and i7 or can be easily upgraded to an i7 (you could also build your own PC) . You can install OS X on the PC using a tool like UniBeast and an external hardrive. You can use your current mac as a monitor. While this will be much more expensive than just upgrading your CPU, it will be much less risky, and future upgrades such as a GPU upgrade will be much easier (along with many other perks of having a PC case to hold your parts).
Hope this can help!