What's the max current on the 5v pin if I use it as an input on Arduino Nano

I have multiple components such as LEDs and Buzzers that is connected to the digital pins of the Arduino, I'm supplying the Arduino with 5v via the 5v pin. However I'm worried that the current draw of the LEDs and buzzer and the controller might be too much for the pin to handle.

Yes.

Read the datasheet.

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"What is the max current on the 5V pin as an 'input'?"
Simple answer: No limit.
You could have a 5v, 10000A supply connected to "5V" (using that as a 'power input' pin).

I would say ZERO because it is an OUTPUT and NOT an INPUT!

I would say : pin 5V can be an Input or an Output, depending on your power supply scheme.

If you don't connect anything to Vin, you can power your card via the 5 V pin. The current limit will be that of the external power supply.
If you put 12 V on Vin and 5V on the 5V pin: boom, you kill the regulator.

If you power your card by Vin, max current will depend on the value of the external voltage.
The power dissipated by the regulator is limited, see the datasheet of the regulator. This power is equal to the voltage difference between the input voltage apply on Vin and output of the regulator, multiplied by the current.
So, if you supply your board with 12 V you will not have as much current capacity as if you supply it with 9 V. This is a thermal problem.

Anyway it's a very bad idea to use the regulator of the card (Uno, Nano, pro-mini, etc) to feed external modules.
A good external 5V power supply is preferred.
A star distribution of power supplies is recommended.

Arduino documentation is false : Imax on an output is not 40 mA but 20 mA.
40 mA is an Absolut Maximum Rating for a short time, permanent use can kill the microcontroleur.
You have also limitation to 100 mA by PORT (8 I/O => 8*20 mA = 160 mA => not allowed by Atmel/Microchip !).

Microcontrollers are not made to provide power

@jim-p
It would be best if it was selectable, the Arduino running from (A) external PS or (B) its regulator and/or USB.
I know that they do 'officially' discourage external 5V application (but I think that's to avoid the mishaps that can result).
On the other hand, the insistence that there's nothing to be had from a stock board is irksome.

@barouyr_88
What can be drawn from the IC (as what you believe to be the 'solution') and what can be applied at the 5V pin are separate matters, essentially unrelated.

Well, the OP seem to be happy with @er_name_not_found's answer whatever that was.

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