You are confusing two different terms. The driver can deliver 5000ma (whether it really can from 3 x 18650's will depend upon the driver design). That is current. The 2500ma of the cell is really 2500milli-amp-hours. It is a measure of the capacity of the cell, and says nothing about the current that the cell can deliver. The 2500mAh cell capacity means the cell can delivery 2500mA for 1 hour. In theory it could delivery 5000ma for half an hour, but unless you using an IMR 18650, it is doubtful you could safely draw 5000ma from most 18650's.
Having said that, the inpput of the driver is probably not 12.6 volts (for that matter at realistic current, it is probably closer to 11 volts under load). Volts x amps= power, so the output
from the driver will be the driver output voltage x the 5000ma. If that is 3.5 volts, than the driver needs 17.5 watts. If the driver is reasonably well designed, it should not take much more than
17.5 watts input, which at 11 volts is about 1.6 amps, and well within the capability of just about any 18650 battery.