These phones aren't nearly as simple to disassemble as they used to be, with all the sealed casings and such. If the Note 5 is anything like the S6 and S7, it'll be a heat gun and lots of adhesive. Even if you could find a good battery, it'd be tough to do the work yourself.
I know it will cost a bunch, but I'd look at contacting Samsung to schedule the replacement. A bonus is that you'd also have a warranty on the battery and the work. If you have insurance on your phone, you may be able to get a replacement device as well.