A couple of circuits that spring to mind. The first was actually for controlling the light output from a laser (amongst other things). Incidentally the laser was used to shine at a turbine blade spinning in a turbine and the optical cable had a return path for reflections back to a photodiode to monitor the timing of the blades: -
![enter image description here](https://i.stack.imgur.com/olOSY.jpg)
The crux of this circuit is the emitter resistor and the feedback control from the op-amp. If you have 1V on your +Vin input (5V before pot divider) then providing you have a collector load, the current will be 100mA. If you have 2V, the current through the laser will be 200mA. With 4V on the +Vin input there will be 400mA through the laser.
Make the emitter resistor bigger for lesser currents and of course dispence with the pot-divider on the +Vin input.
The 2nd circuit is this; it's a power output stage to an op-amp based arounf an NPN BJT transistor and feedback to the opamp to provide regulation: -
![enter image description here](https://i.stack.imgur.com/puy3A.jpg)
Quite simply the feedback on the op-amp tries to maintain the emitter at precisely the same voltage as Vin. This will give you the power for driving your laser.
Things to watch - the laser forward voltage needs to be accounted for as does the heat dissipation in the BJT and the emitter resistor in the 1st example.
Insert a 100 ohm or so resistor in series with the LED, to limit the current if you get the transistor fully turned on.
Disconnect the audio signal for now.
Instead of your BE and BC resistors, use a pair of resistors, one from B to +5, and the other from B to ground. The ratio should bias the base so that the LED is just dark. That should be about 10k to +5 and 1k to ground -- but adjust until the LED is slightly off.
4 Connect the audio to the base via a capacitor -- this is actually the crucial ingredient. A range of values will probably work -- say 10uF. That will be polarized -- the + end should go to the base.
That should be much more sensitive than what you've got. Your main issue is that the audio is likely at zero volts, and so you need about 0.5V to 0.7V peaks (on the positive side) to get the transistor to turn on. Using biasing resistors and AC coupling with the cap means you need much smaller +ve peaks to get some LED lighting.
Best Answer
You need a diode across the relay coil to handle back EMF or you may destroy the transistor. Ignore the LED in this picture