the i5 will basically double the cpu performance--2t/2c vs 4c/4t. the i7 adds ht on top of that (4c/8t)--won't double performance again, but expect at least another 50% increase over the i5 for most multi-threaded workloads. if you can get the chip cheap, go for it. it's an easy upgrade. 15-20 & 40 (usd) seems to be the 'fair' used price for them. same tdp so the existing cooler would work, but clean the surfaces and put on new thermal paste.
otherwise, if you want an 'excuse' to start looking for something new and significantly faster, here's your chance. :) start pricing out an even newer and faster minipc to replace what you have. but do keep in mind that going 'too new' will also require different ram--but you could also gain an nvme slot, and better hardware decoding/encoding for your future streaming media server.