Plutarch says the Egyptian year was 360 days until Thoth gambled with the Moon, won a seventy-second part of every day, and assembled the winnings into five extra days.

The five epagomenal days were when the great gods were born, and they sat outside the calendar proper. Thoth was god of writing, reckoning and the Moon, which is a combination that makes sense the moment you realise that counting months was the original reason to write numbers down at all.