The e28 M5 is the father of M5's. its the car that started it all, and its build to LAST, IF maintained properly. I can go on and on, but ur not looking for history:
Here is some things that you definitely need to check out, that go on ALL e28;s
1) Front arm bushings (mine were gone about 300$ labour/parts)
2) Rear Guibo's (mine were gone, about 120 per side labour/parts)
3) Head gasket (if the car was BEATEN like mine was, ur not onl looking at an head job, but an entire rebuild, which costed my car's previous owner just a little under 3K to do.
4) Rad/thermostat/etc. E28's tend to have overheating problems.(mine did, and reading some other e28 boards, others do too.(let the car idle for some time to see if it overheats
5) LSD (apparently mine had it but it was ****ed)
6) Bearings like to go as well(about 200 a side)
7) ELECTRICAL PROBLEMS and thats A MAJOUR one with the e28's and old 7 series. Anything from small things like lights saying that ur break lights dont work (when they do), to ur auxhilaryu fan going, sunroof going, ac going etc (happened to me, and 250 $ later, NONE Of them worked.)
8) rear springs tend to corrode and break when doing hard ornering/donuts/ burnouts etc (not that this happened to me
9 Cruise control
10) Sluggish shifter (from years of wear, and no replacing of the rubber components)
11) holes in the floor (just about anywhere)
Theres more, a lot from experience, and a lot ive read, so ill post them as they come to mind. actually, i wouldnt mind coming to look at those cars with you. M5 ARE NOT something you want to neglect REALLY looking at....... So let me know...