The LED is connected to the same 5V pin as LCD.
If I disconnect the LCD's connections going to RPi (RS, EN, D4-D7) it turns off.
But if I disconnect just a 5V wire (connected to breadboard) the LED stays turned on.
I think that the voltage comes from one of the RPi's pins to the LCD? And then to the LCD's 5V input (through the LCD's circuit)?