I have a battery pack used to charge mobile phones. It's capacity is 13,000mAh and it has two output ports. Both are 5V but one is 1A and the other 2.1A It also has an Input port of 5V 1A. (To which I will connect a solar panel).
If you have a circuit diagram for your 13,000mAh 5V battery, check whether there are internal connections at higher than 5V. Because 5V is not a common battery voltage, there probably are cells in a higher-voltage series connection, being converted to 5V output via a step-down (buck) circuit.
An item like a “5V DC to 9V DC Converter DC-DC Isolated Power Supply Module” as in picture below [from ebay seller bidcenter] might do the job. Also available are less-expensive not-potted adjustable boost regulators.