What you ask is very relevant and is important to understand many electronic topics. It is related to the resistance and impedance (fancy name for AC resistance) of the pins, in this case, involved in the connection of one circuit with another.
You measured that the input resistance of the of the 5V pin is about 3KΩ, when the Arduino is off. That is not very high, but it is not a input signal pin.
In general input pins should have a very high impedance, several MΩ, to avoid impacting the level of the signal that they get (e.g. a weak signal of an small sensor). And output pins should have a very low impedance, to provide a strong signal that can drive the next circuit without problems.
Inside the Arduino (or any other circuit), behind a pin, you don't know what is connected. And usually there are a lot of transistors that will change the paths of the current dynamically and it's own characteristics. But you don't need to measure or do the maths, in the datasheet usually the input or output impedance is specified, when relevant.
A circuit can be simplified statically as an equivalent resistor + capacitor + inductor. Or simplifying more as a load resistor.
And the resistance/impedance is important, to know what will actually happen when you plug your circuit there (or your resistor). And your circuit will have also its own output impedance.
Ideally you will always want to connect a low impedance output to a high impedance input. And this is valid for the Arduino pins also.
For example, when you create a voltage divider and connect it to an analogic input pin of the arduino, it will work only because the pin has a high input resistance, about 10MΩ. Otherwise the internal resistance of the circuit behind the pin would be in parallel with your resistors and screw up everything.
The same that you observed with your resistor, because the 5V pin has too low resistance compared to the resistor value.
