yesyes wrote about depletion mode MOSFETs, " They need a negative voltage. I would have to generate that just for the MOSFET."
No they do not require negative voltages. The depletion mode mosfet has a negative threshold voltage. It has a conductive channel when the gate voltage is the same voltage as the source voltage. If the source voltage is 3 volts, the gate can be 0.0 volts to turn it off.
Connect your LED to the depletion mode MOSFET source
connect the FET drain to the 5v VCC.
connect a 680 ohm resistor to the led and to ground.
ON gate = 5v
OFF gate = 0v
See , no negative voltages. The diode drop in the LED is about 2v , so the MOSFET is off whengate is 0 and source is +2v. The negative voltage you mentioned is only needed if the MOSFET source is near ground voltage. But in this high side switch, the source is not at ground, it is over 2 volts, so the MOSFET can be turned off.
The circuit by pelleplutt is good, using an npn to be off when power is on but Arduino is unpowered.