HC-05 Bluetooth Module - External Power

I wrote a Code for Control LED Lamps for model Car (via Bluetooth) . When I am powered up the HC-05 module through Arduino Uno board , All works perfectly.

But later I decided to save my Uno module's working power . So I gave external regulated 5V to HC-05 module . "+5V to VCC" and " - to GND" .

But when I powered up the circuit , Arduino board is not responding to the Bluetooth module (All indicator lamps on BT module and Uno are working). (Phone also connected to the BT module)

Then I reverse the process and set my circuit to previous working mode (Uno is powering up the BT module) . And its starting to work perfectly.

Did you connect GND pins of both devices?
Give your wiring diagram.

I can not see ground wire between Arduino GND and HC-05 GND!

I agree, a GND wire from the Arduino to the HC-05 is needed. Not to carry power, since your Arduino appears to get 5V from the Relay Module, but to provide a Ground reference for the serial signals.