Being one of the few who raced a YZ80 around here in the late 80s, I can tell you a few things about this bike. First off, echoing another poster, 1986+ YZ80's have a disc brake in front. 85 was the first year for the white plastic/red frame in the states (canadian and euro models had white plastic since the 70s...US had yellow through 84).
If your YZ80 had a red frame, no lower gas tank extension on the right side (petcock side, it should extend down whereas the -85 models did not), and a drum brake it is an 85. disc brake? 86.
The 87 YZ80 had very minor changes over the 86. In fact, the same aftermarket pipe can be used for all 86-92 models. Actually, the bike in general changed only a small amount from 83-92. I don't know why Yamaha gave up on the mini class in the late 80s but they did. They went from absolutely owning the class (and the 60 class in 81 and 82 with the YZ60 til the KX60 came out in 83) in the early 80s to handing it over to Kawasaki and Suzuki (KX80s ruled in 83-85, RM and CR80 after that with the YZ80 falling behind more every year). This generation of YZ80 had pretty antiquated suspension by 1990..essentially identical to the the 83.
Things to be aware of: water pump impeller gasket, also the common problem where coolant gets in the crankcase and makes an ugly sludge the bike will spit out the crankcase breather hose. The Z spokes on this bike are also typical 80s Yamaha annoying.
The smaller size of the bike makes it a great playbike or for those too big for a 60 and too small for most other 80s. A stock 87 CR80, when they were new, was almost 6 mph faster stock for stock, with stock gearing. Yikes. However, my bike even stock held its own on tight tracks, especially going up a few teeth in back (if i remember right, these bikes have something ridiculous like a 46 tooth rear stock). pipe, silencer, fresh rebuild, some porting and boyesens really woke it up...we also used to drill holes in the airbox the size of quarters and cover on the inside with fine mesh to get more breathing. Yamaha also sold an optional stiffer rear spring, might still be available.
Given that the bike is 99.999% the same as a 1992 (the 88 got a new flat top piston and perhaps some changes to the head/squish band?), and that there are billions of these bikes out there, parts should not be a problem.