Yes you can charge it. You have to use a car specific battery charger which can range from something like 10-20 amps. The higher the amps, the faster it will charge the battery.
To find out how long to charge the battery, you will need to find out the capacity of it. I am unsure as to how big the capacity of your CX-5's i-stop battery is (we do not have i-stop in the states). Chances are it probably won't be too much more than a 120 min reserve capacity. Using a volt meter, test the battery. If it is around 12.5v, it is around 50% charge. At that with a 10amp charger, it will take around four hours to charge a 120min reserve capacity battery. So with that said, use this info as a basis.
... Or just go to your dealer and have them take care of it.