A little quick math shows why that's probably not going to happen any time soon...
At 20 mpg, a car uses about 333 kWh (kilowatt-hours) of thermal energy - in the form of gasoline - to go 200 miles, as you suggest.
If we assume the engine and power train are about 15% efficient, that's 50 kWh of actual mechanical energy delivered to the wheels.
To put 50 kWh of electrical energy into a battery - at a recharging station - in five minutes, would require
50 kWh * 12 = 600 kW
of electrical power. That's a bit more than 2700 amps at 220 volts. The factor of 12 is because five minutes is one-twelfth of an hour.
And that's assuming that electric vehicles are 100% efficient from the charging station to the wheels on the road. They're actual efficiency is quite a bit less than that. I would guess that an overall efficiency of 80% is probably being generous. That would raise the current needed to charge you up in five minutes to about 3400 amps at 220 volts.
Keep in mind that the typical arc welder operates at something like 400 amps. Picture the cables and connectors used for a normal shop-floor arc welding setup. Now multiply the size (area) of those cables and connectors by almost nine, and you've got the size of the cables you'd need to carry the current necessary to charge your car in five minutes.
Not to mention that six or seven hundred kilowatts is probably something like twenty times more than a typical gas station uses overall, and then multiply that by four or five cars wanting to rapid-charge at the same time, and you can see the problem.
Why electric cars will never be mainstream.
IF capacitors could be advanced to the point that a 200 mile range or more would be available in one or two capacitors, why couldn’t there be an exchange system, so the car owner rents the capacitor and pays for the charge therein. Exchanging capacitors would solve the ‘quick refuel’ problem.
I believe those amp requirements exceed what is used in a large MRI facility which the breakers where at 2200 amps if I remember correctly. (also at 480 V 3 phase)
Current DC quick chargers allow you to add over 200 miles of range in about 20 minutes and in the case of Tesla’s you don’t pay anything for that. Yes that’s still slower than filling up with gas. But with Tesla its free. 5 minute fill up for 50 bucks, vs 20 minutes for free. And don’t forget with an EV you wake up with a full tank each day.
I'm not arguing for the technology, but I can envision ways to make it more efficient at the nuts and bolts level.