After spending your career as an AI Data Trainer, you decide that a change of pace is in order and you might as well become a pirate. You entrust your first mate with a chest of gold coins to bury for safekeeping. The chest is brimming with sacks of $40$ coins each. Five days later, your first mate reappears with a wild tale of being ambushed by a band of $14$ rival pirates. According to his account, the pirates distributed the gold coins as evenly as they could amongst themselves, but ended up with $5$ coins they couldn't divide, which they then flippantly tossed into the sea. 

Now you're faced with a choice: do you believe this extraordinary tale or is it time for your first mate to face the plank?