There is a consideration not addressed here and that is the regulator. Theory say's a linear regulator (7805) is a voltage controlled resistor. So you have X load current(batt) @ Y Votlage ACROSS the Regulator 9.6V? - 5V = 4.6 V X total load current, one figure I saw was 180 mA... .18 A X 4.6 volts = ,8+ watts wasted heat in the regulator and it takes Battery Power to make that heat, power that doesn't get used in the load but wasted, What's worse is it is your available current going up in heat. There is a simple and easy to implement answer that will waste less than 5% instead of the nearly 100% loss you have now.
Several stores on Ebay sell Adjustable 1 - 2 A Buck mode switching power supplies that are about 25 mm on a side and are capable of 95+% efficiency and not a lot more than a 7805... I bought 3 @ $1.80 Ea
You can also buy adjustable boost mode type switchers that would let you run your project from 3 Alkaline "D" Cells It is the method I use exclusively the parts are too cheap and too easy to use, require no output bypassing and are stable until the batteries are exhausted. The benefits are obvious, almost twice the available battery life and no need for Big battery packs. IMO
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