Schematics say “5V / can also be 12V”. Recommended range according to the Nano spec is 7-12 V, so +12 V is ok but 5 isn’t.
(the Nano FAQ says 6-20 V, the ATmega328 can run at 4.5 V but you won’t get 5 V out, and 20 V is absolute max for the regulator, but then it has to burn away a 15 V drop so you risk frying it if you add any non-trivial load.)
EDIT: To clarify, the ATmega328 can run at voltages below 4.5 V but not at 16 MHz according to the specs, which is why this kind of works until it doesn’t 