Here's some rough numbers:
Assuming a 55KWhr battery similar to the Tesla Roadster; You've got a pack that takes 4hrs to charge at 80A (220V); that's 4hrs of power at 17½KW or, 70KWhrs of power. (Note that the extra 15KWhr disapears as heat).
If you wanted to charge in 5 mins at the same 220V, you'd need to get a supply at a smidge under 4,000A... Most US houses have a 200A feed... and the wiring would be like railway tracks!
If you wanted flexible wiring at say 80A then the voltage would need to be 10,500V. That would be risky; at that voltage the insulator has to be impecable; just the slightest crack in the insulation and the sparks would fly.
Some middle ground like 200A at 4,000V that was connected to the car by an automated robot arm or underbody connector might be fairly cheap to design and install; and by cheap I'm thinking a few thousand USD. Flip over a ScaletriX slot car for a design prototype example.
In the US, the next step up from Home and Office supply is called Primary Customer, and that offers 13,000V and 4,000V feeds; the 4,000V feed can be ordered online!
I'm sorry, hydrogen to power a car??? What next Custard to power space rockets?