NPN Transistor For 3 volt base to switch/control 5 volts
You need a PNP transistor ideally controlled from an NPN transistor.







simulate this circuit &ndash; Schematic created using CircuitLab

The reason why a single NPN emitter follower doesn't work is because the emitter output HAS to be lower than the base (3V) to get any current passing from collector to emitter. So the emitter might be 2.5 V when base is at 3V and collector is 5V (or greater).

You might be able to use one PNP transistor with appropriate potential divider values or maybe a small zener diode and resistor on the base to the GPIO.