Phones typically have batteries of between 1Ah and 2Ah capacity. To charge a 1.5Ah battery in five minutes would require a current of 18 Amps. That is way beyond the capability of a typical USB or similar charging lead. I doubt if a suitable connector could even be provided without making the phone somewhat larger.
As for electric cars, it's the current carrying capacity of the supply cable that typically limits the charging time, so a battery capable of being charged faster would not necessarily be any advantage. A megawatt charge rate would for example require a 25mm cable (the size of typical house supply tails) but with 10kV on it. Lower voltage would be safer but the strength required to manipulate the even heavier and very stiff cable would be a real problem.
For comparison purposes the energy density of petrol/gasoline is about 45MJ per kg -equivalent to a Megawatt for 45 seconds- and a typical hose can deliver several kilograms in 45s. Which equals a multi-megawatt energy delivery rate, achieved with reasonable safety (Smokers might earn a Darwin Award, but that's their problem) and no need for the strength of a gorilla to hook-up. Kinda hard to compete with.