35 years ago, Michael Jordan -- a junior hoops star at the University of North Carolina -- hustled a UNC student on a billiards table ... and was paid his $5 winnings by personal check.

Now, that check -- made out to and endorsed (signed) by "Mike Jordan" -- is on the auction block at Goldin Auctions.

According to the auction site, the story goes like this ... and it's pretty awesome.

It was February 27, 1984 and Jordan -- in the mood to play pool -- went to the basement of the Granville Towers on UNC's campus ... and proceeded to dominate on the table.

The guys were betting money ... and MJ was up $25.

A friend of the guy Jordan was beating thought Michael was hustling his buddy, so he stepped in to play MJ ... and win back some of the money he'd lost.

MJ lost a few games in a row -- which the consignor says irritated Jordan -- so he decided to cash out and take the 5 bucks he was owed.

The friend -- realizing Jordan was likely going to be an NBA superstar -- asked Michael if he could pay him with a personal check.

Michael accepted ...and the UNC student wrote the check to "Mike Jordan" -- the name basketball phenom went by on campus.

The check -- drawn from a First Union Bank account in Pembroke, NC -- was cashed by Michael and ultimately returned to the consignor.

The UNC alum held the check for over 35 years ... until recently deciding to put it up for auction.

Goldin says MJ's signature has been authenticated.

Auction opens November 18.