You haven't disclosed the size of the chicken coop. Judging by the amount of light you can get out of a car battery, it might not be all that big.
What's it cost to move the chicken coop?
What's the cost of 5 miles of wire? Assuming you own the land between. Maybe there's a fence you could run the wire along. Run 48VDC with some kind of GFI-type breaker. Available power might enable other improvements.
I can think of only two ways solar can win.
1) if you can get some other taxpayer to pay for it. 2) there ain't no other way.Can you import some endangered species and convince the government to require the utility to extend the reach of electrical power to prevent extinction?
Solar power doesn't have to be photovoltaic. In Arizona, you might have enough thermal differential to use a small reflector and a stirling engine.