Power supply short circuit protection
If you want a LED lighted when there's a short circuit you can place the LED at the 7805's input, and control it with the 7805's output voltage. Use a PNP transistor to switch the LED, and drive it from the 5V output. Since the input voltage is a few volts higher than that, you'll need a voltage divider to the base to prevent the LED from lighting at 5V out. Placing the LED between emitter and input voltage also helps, though the divider is still required if the input voltage is several volts higher than 5V.
If the output is shorted it will go to 0V, and the PNP transistor will be switched on.