ANCHORAGE, Alaska — The $5 bill displayed for decades on Charles Fairbanks IV’s wall was long a treasured family heirloom from Alaska. Now, to the surprise of the grandson of a turn-of-a-century vice president, it’s also become a likely treasure trove.

The rare find is expected to fetch as much as $300,000 at auction this month when a Texas auctioneer plans to put it up for bids in Dallas and online as part of the American Numismatic Association National Money Show....