Best to buy another that doesn't have problem. You can get an F5 in excellent condition for $500 or less. I do not think replacing the motherboard would be less than that.
Robert's camera (usedphotopro.com) has an F5 parts body for $163.00 usd.
As for someone to do the swap, I'd contact Zack's, though I don't know if it's something he'd tackle.
Have you had anyone diagnose it? The actual problem may not be the main board. Also, how much power is it consuming? Does it function correctly otherwise?
Exactly how much current is drawn when the camera is turned off? It may not be all that bad. Just have to remove the batteries when not in use. You should remove the batteries any way as alkalines tend to leak.
It was once diagnosed at Nikon's service center and they said that the motherboard must be replaced.
As for power consumption, it will reset the batteries or rechargeable batteries in 2 days max. I checked on both of them. Everything else works great. I have the back panel of the MF 28 and there is no current going out of it
There used to be a recommended Nikon service in England. Unfortunately, I do not remember his name , but a lot of equipment people from Poland sent to him, because he was and cheaper and undertook repairs that in Poland service refused to perform - as a rule, in Poland they always wanted to replace the entire systems
Definitely the easiest thing to do is buy a really nice one from a Japan seller on Ebay. There's so many beautiful cameras coming out of Japan, for very affordable prices.
Or just put in your batteries when you are ready to shoot