michinyon:
I don't think there is any such thing as a 5V lithium ion battery.
Depending on the chemistry, battery cells have a characteristic voltage based on the chemistry, and multi-cell batteries are multiples of that voltage. For example, Lipo batteries have a nominal voltage of 3.7 volts, or 7.4 volts, or 11.1 volts ..... not 5V
Also, the capacity of a charger is determined by it's current supply ability, not the size of the battery. For a specified charger output current, bigger batteries just take longer to charge.
3.7 volts would be fine. I just don't want to use a polymer battery because of the fire danger.
Lithium-ion and lithium-polymer batteries share the same concerns as far as charging/discharging/fire risks and other safety concerns. The poly cells tend to have more vulnerable packaging so possibly more vulnerable to mechanical damage, but both need the same care in charging and discharging practices.