You can use a 5V output powerbank to charge your battery by using a relatively low cost after-market charger which is designed for this specific purpose. Thomas's answer is essentially correct if the original charger is used but the devices described below provide the 'missing link' to make it possible.

Other single cell Lithium Ion batteries can be charged by similar means.
In addition, in emergencies, it is possible "with a little care and sensible treatment, to make emergency chargers that allow any single cell Lithium ion battery to be charged from any 5V "USB" power source.

As an example of a 5V input charger that will meet your need, this charger accepts 5V input via a micro USB connector and charges your model of batteries. Also, if you have a solar panel that provides 5V USB output (as many are designed to do) then they too could be used with this charger.

A number of other chargers which may suit can be found here

This solution is workable because:

A single cell Lithium Ion battery has a voltage range from 3V fully discharged to 4.2V fully charged and an average working voltag of about 3.6V. This explain why such batteries are usually labelled as being "3.6V" batteries (sometimes 3.7 V) and the charger is said to be a 4.2V charger. Usually the batteries are charged at a designed constant current Imax (= Constant Current or CC mode) until the voltage reaches Vmax (usually 4.2V) and then held at a constant 4.2V (= constant voltage or CV mode) until the current falls as a result of battery chemistry to some predefined fraction of Imax. To allow the voltage to reach 4.2V slightly more than 4.2V is required, to allow for voltage drop in the charger circuitry. The ~= 5V from a USB charger is enough.

Larger cameras (eg DSLRs) often use 2 x LiIon cells in series to give a nominal 2 x 3.6 = 7.2V battery with Vmax = 8.4V. The voltage required to charge these is > the 5 = 7.2V battery with Vmax = 8.4V. from a charger or USB port so a USB supply cannot be used directly. One solution is to make a boost converter to provide the > 7.2V voltage required.

Emergency 1 cell charger: Later ...