EBike Controller - Does 'current' affect driving speed?
To a first approximation (a flat, level road), increasing the current capability (not the current) will have no effect on your speed.

A BLDC motor is effectively driven at a certain AC frequency, and the motor turns at one revolution per cycle of the drive. As long as the motor gets enough current to produce the force necessary to overcome friction and drag, increasing the current available won't change anything. And you should note that, from a power perspective, it's clear that your battery and motor are well-matched. The motor is rated for 5 amps @ 48 volts (peak 10 amps), for a total of 240 watts (480 peak). The motor is rated for 250 watts, so the motor is the limiting factor. 

So the first thing you would need to do is replace the motor. However, you would also probably need to replace the controller as well. I suspect there is a speed limiter somewhere in there.