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Im not sure Intel has any worthwhile CPU’s unless you are getting them used.
Currently E cores are mostly trash, and not all that “efficient” and letting a P Core turbo up and get the task completed uses less overall power.
Secondly Intel is lying about its heat output, and power use. Everything from 10th gen up is a power hog if you dont limit the performance to well below “stock” settings.
https://www.techspot.com/review/2612-intel-core-i5-13500/
This is a good match up between an i5-13500 vs R5 7600, which is the most interesting IMO. The R5 7600 seems to be about $15 less expensive for just the CPU and uses 3/4ths the power which will be a greater savings over time vs Intel. The AMD Motherboards also still seem to trend a bit lower in cost than Intel.
So overall its a good question. If you can get a use 13500 or one under $150 then its probably worth it, but at retail prices the 7600 will cost less to buy, and less to own while being similar in performance.
many times, shucking is a very valid way to get large format disks for cheaper than retail NAS parts. But be aware of what your buying and make sure that the disk your getting if its a white label is a reliable disk. WD Easystore/Mybook are generally good, as are the larger format Seagate external.