Hello, I just recently bought a board off of eBay and it’s the Intel DH57JG Lga 1156. I’ve looked at supported CPUs on Intel’s website and it only supports lower end i3 and i5 CPUs. I’ve heard on other threads that they have put in an i7-860 or a Xeon x3470 and worked perfectly. Some people said it will not work though. I honestly have no clue if it will work or not.
According to the spec datasheet that board only supports CPUs with a TDP up to 87 Watts. The Core i5 7xx and Core i7 8xx are all 95 Watt TDP CPUs, so even if the board did boot with them you may encounter throttling under heavy workloads due to the board's weak power delivery not being able to keep up.
You can give one of those higher TDP CPUs a shot if you want, but you're probably going to want to use a downdraft cooler or add extra fans to provide additional airflow over the VRMs surrounding the CPU socket. You can also forget about overclocking.
In any case, all of the available CPUs are going to be 10 years old and aren't great performers these days for the most part. Depending on what you plan to do with this PC, you may be better off trying to track down something more modern.
If you really need something with quad cores, stretching this intel board with a higher tdp processor will still be sub-par for today's environment for anything needing quad cores. The lga1366 or lga1155 platforms will provide a lot more performance.
However, if whatever you are doing needs just a few cores and high single thread performance, the i5-680 is a miracle chip for this platform. My i5-680 systems feel almost as fast as my i5-2500 ones.