How long will it take to? 500 kms of wire, 1 curcuit breaker at one end and light at the other end.

How long will it take, once the breaker is on for the electricity to travel 500kms to turn the light on.

There are two different subjects here:

1. How fast do the electrons in the wire move?
2. How fast does the electromagnetic signal move?

The electrons in the wire move quite slowly but the signal moves essentially at the speed of light. The situation is sort of like water in a pipe. Although it may take a long time for water at the reservoir to reach your house, if the pipe is full of water and a valve is turned on at the pumping station, you will feel the pressure at your house very quickly (like at the speed of sound in water).
Therefore assume that the signal travels doewn the wire at essentially 3*10^8 meters/ second and has to travel 5*10^5 meters

5*10^5 / 3*10^8 = (5/3) * 10^-3 seconds