What size equipment grounding conductor is needed for this gate lights circuit?
Where the grounding conductors are increased in size (from the minimum) the grounding conductor also needs to be increased in size proportionately per 2014 NEC 250.122. I used the southwire voltage drop calculator. The calculated value needed for a 5 amp draw is #8 copper for 5 amp load at this distance 2.8% voltage drop. The problem with down sizing the conductor in this case would come if the lighting was changed at a later date using more of the available ampacity of the circuit then the conductor would be under sized. 120V @ 12 amps would require a #4 conductor and the #8 would be two small to limit the voltage drop for a short circuit.