The guy who buys up private watches and then lists them on eBay is back again. Among many other watches, he lists a 5513:
https://www.ebay.com/itm/274844908440
The case is incredibly sharp, so I asked a dealer friend if it looked fake. He said it looks genuine, but pointed out the 5 o'clock lug. Oops. Guess I'll take that off my eBay watchlist. Photo below.