you might be right but it is not my problem. my problem is about voltage drops when connecting the lcd board. if the current is below the quiescent value, then my regulator would not give 5 volts when nothing connected. but it gives 5 volts. so, ı think the problem is not about the current value.

That is what he is talking about. With a 1 kΩ resistor, you circuit can only pull 10 mA before the regulator becomes voltage-starved. It's actually a bit worse than that because your current draw isn't steady and so you will get peak currents higher than average. The regulator circuit itself draws about 6 mA (that may depend on manufacturer). So, with nothing connected, your regulator circuit can work fine. But when you connect something that draws more than a few milliamps, the regulator starts dropping out.

This is why it is important to show the circuit you are using and not something that leaves things out.

Do you have ANY other 5 VDC source that you can use to power your LCD board to verify that it is good and to measure how much current it is actually drawing?

Can you measure the input voltage to the regulator both with and without the LCD board connected?

Do you have some resistors that you can use as loads for your regulator to map out its actual performance in order to find out how much current you can draw from it before it starts dropping out?

Can you bypass your 1 kΩ resistors to see if that will let your regulator power the LCD board. It doesn't have to be connected for long to determine if it works or not.

 

Your 1k resistor in series with the voltage regulator IC causes it not to work properly.
The input voltage to a 7805 or 7905 must always be at least 7V.

Measure yours, its input voltage is reduced too low by the 1k resistor.
The LCD device's load current in the 1k resistor also reduces the regulator's input voltage.
Here is the datasheet recommendation: