I suspect with 5F load across a 7805 it will struggle to keep it's output up anyway. For a significant time it will be in current limiting state.
The problem I see with balancing resistors is they would need to be very low value to ensure each capacitor sees an equal voltage, there is no margin for error, if the voltage isn't equally shared, one of the capacitors will go pop! I'm thinking (without doing any math) the resistors may have to be 10 Ohms or less so they will use much of the 7805's capability before even starting to charge the caps. From the first post, I'm guessing the 7805 is also powering the remaining circuits as well.
It's a tricky problem, I think the best solution may be to simply add series diodes across the capacitors, so they work like Zeners but only using the 0.6V - 0.7V Vf stacked up instead. Four 3A diodes in series across each capacitor would probably work. To get an exact voltage it may be necessary to mix normal and Schottky diodes.
Brian.