This was the car that pretty much every car enthusiast I knew was shopping for twenty-one years ago. The ones who bought them had short honeymoons. It's amazing how fast, 'I'm going to keep this car forever!' turned into, 'I went back to Mercedes-Benz(or Lexus).' A guy in my office bought one over a Ferrari thinking it would be a more practical choice only to have the clutch, differential, and then gearbox need replacement before the first oil change. His previous car was a 6-speed, twin-turbo 3000GT or Stealth; so it wasn't a matter of not knowing how to drive a stick. Another friend went from planning on buying a second one for his country home to deciding not to keep the one that he had in a few months. E39s were beautiful cars that drove brilliantly, but they aged like milk. I can't conceive of the proper level of humidity and combination of protectants that would keep the engineered biodegradation of the materials used in these cars from occurring.
That's a very different and outlier experience from what I have seen in the e39 M5 community. My car was quite reliable, in reality the engine is under-stressed at 400hp for a 5L motor. I really only had two kind of failures over 12 years and about 80k miles. One was the instrument cluster lost a couple pixels, it was replaced under warranty. The other was a MAF sensor that went bad, but I bought a VW equivalent and solved the problem. Other than regular wear items like tires, wiper blade kind of things it was an extremely reliable car.... surprisingly unlike my wife's Honda Accord with overheating problems, CV join issues etc...
On the other hand a 3100 mile car probably sitting for 17 years mostly undriven could have hidden problems for sure.
That's a very desirable car. If you take good photos and videos (or can pay someone to do it) I'd recommend selling it on Bring a Trailer or eBay. I would also try E39 M5 forums and Facebook groups, which might find you a good buyer without the hassle and expensive auction fees.