I like being able to charge that rapidly. However it does not seem to be practical for widespread installations. The numbers just don't add up.
A cheap (Leaf, eGolf) EV has about 20-30KW battery (giving 80-130 miles range).
The current widespread commercial chargers are generally 6KW (the kind you find at parking lots, offices, etc). They will charge the car in about 4 hours from a depleted state. (The home chargers are 3KW or even 1KW but let's ignore them for the moment). To get 6KW, the charger supplies 204V @ 30A. (For a comparison, the only other device at your home would be the oven or the dryer that is using the same level of power).
The "superchargers" provide about 100KW (they range from 30KW - 120KW). To do this they use 408V @ 100+A. However they require commercial installation, since this is more power than several houses combined together. They allow charging 80% of battery under 30 minutes for the smaller cars. Teslas are at the high en of the spectrum (120KW), and they can charge the 60KW versions in just above one hour.
To get 5 minutes charging we would need to jump to 1,200A @ 408V, or 100A @ 4080V. The first choice is not practical. (At 1m this requires a cable width of 50cm! / 20in). The second one requires larger electric components in the car. Also even with 1% loss due to heat (which is wishful thinking), the excess heat would be 10KW, which is in the commercial oven range (i.e.: standing near the cable / car would easily roast a chicken, or make kabobs).
Overall it is nice to think about these technologies, however there are limits in physics that make this very impractical in the short future.