500miles/60mph = 8.33hrs
12kw x 8.33hrs = 100kwhr
5min/60min = .083 hrs
100kwhrs / .0833hrs = 1200kw
1200kw at 600 volts dc = 2000 Amps
So in order to charge you vehicle in 5 min you will need to darken the surrounding neighborhood. And yes, plug in a cable the size of Hillary’s thigh.
I would not recommend doing this in the rain.
The math is correct. It's the "how much power does it take to move a car 500 miles" that's in question.
You say 12 kwh (16hp). Another poster said 45 hp. Another, 6hp. For a car people would buy (not some three-wheeled, fiberglass experimental 2-seater), I'm guessing it's in the 20-30 hp range.