Accidentally left external 5V connected to input pin while Arduino is off

I left a 5V source connected to my input pin while the Arduino is powered off. Will this damage my pins? the 5V source turns on every 3 hours for about 30mins.

Is anything else connected to the Arduino ?

there is a GND and an output pin connected to a digital input of another controller which should have no voltage on that controller's pin. other than that, no devices.

is the GND the same GND as the 5V signal ?

yes

In theory, when the Arduino is off, your circuit will power the Arduino through your pin's protection diode. This is not good for your Arduino.

but no immediate damage? because i won't be able to go back to power the 5V off until the next day. this is a very rare occasion (first time now that it happened).

Hard for me to tell... I'm more of a Software guy than a hardware one...

it's been discussed before, read this

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No way to know. phantom-powering like this can lead to damage, perhaps of just the pin's pad-driver, or the whole chip (typically if large currents flow and the chip enters CMOS-latchup.) Or you might be lucky - it depends on the amount of current and how rugged the protection diode is on that pad.

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Generally this will damage the port pin. It may not fail immediately but eventually it will fail, this could take years. Failure could be an increase in leakage or a catastrophic failure of any part of the port. Best is to have a spare.

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I'd suggest to protect the input. You could use a simple single Transistor inverter or an optocoupler (which is a good idea for external signals anyway.

Whether damaged or not, you should as a minimum use a series resistor of at least 4.7k at each input. The resistor should be relatively near the Arduino.

Best way to tell is to power it up correctly and see what happens. I've found them to be remarkable resilient.

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They definitely are quite resilent. But neither "Testing" nor relaying on "Resilence outside stated parameters" is generaly a great idea. Yes, you can run an Arduino powered over a data pin but it's not a good idea because it might lead to failuere and/or (even worse in many cases) unexpected behaviour.
I've encountered ATMEGA2561 processors (used on the Mega, but it was on another board in my case) that had problems writing to eeprom or flash or loosing memory contents. The reason could have been that the supply for the analog part of the board had failed and the ATMEGA was feeding that circuitry over the Aref-Pin. I have no possibility to say for sure, that this was the cause but here was a correlation because several boards with those memory problems also had the failed analog supply.
And that's the problem. Sometimes it seems, that everyting runs fine if we run it out of spec. But we can't be sure that everything runs fine and that it keeps running well for extended periods of time. We are not able to assess, how close to the breaking point we are.

Oh, and I can say from experience that the Arduino MEGA 2561 v3 does not like +24V on the Aref pin. Surprisingly enough, I could still programm them and they were somehow running, but some outputs would not work at all, some only with halve the voltage or only if some other pin was enabled as well... (I had managed to get an LM7805A to fail short, but that's another story)