In my previous post (#3), I missed the requirement to charge for 10V using a 5V source. In this case, balancing the capacitors during the charging phase does not apply since the capacitors are either charged individually or in parallel (see the concept in #6) from the same voltage source. Then, the problem becomes how to maintain balance during storage when unequal leakage currents will unbalance the capacitors over time. If the capacitors are kept at equal voltage during the storage phase, then, during the discharge phase, you can get the most energy out before any imbalance can cause reverse charging (see post #6). So, some sort of passive or active circuit is used to maintain equal voltage between the capacitors. These networks basically transfer charge between the capacitors to keep them at the same voltage. Yes, there is energy loss but hopefully more of the energy can be used in the end.
BTW, in practice, when going from a lower voltage (5V) to a higher voltage (10V), are switching schemes used or is a boost converter used to increase the lower voltage before charging the caps?