> this is that a 5 V battery is more "powerful", so where the hell is that 
> extra energy going to come from?

You'd might think of it in wattage or VA terms. Power = Power on
both sides of the equation because of conservation (ignoring losses)

1 amp supplied from a 1.5V battery (1.5W) has the same energy
as 0.3 amps from a 5V battery
 
> So is that how it all works? If you want to use a single AA battery to 
> put 25 mA through a 200 ohm resistor then:
>     * 87 mA has to come from the AA battery
>     * The regulator steps up to 5 V and gives out 25 mA

25mA into 200 ohms dissipates P = I*I*R = 0.125W

So ideally you need 0.125W from the1.5V battery

P = I*V, 0.125 = 0.83A, 83mA. But efficiency is 95% -> 87mA

> Let's say I have two AA batteries, each of which is 500 mA hr. If I
> put them in series to form a 3 V battery, then what's the capacity of
> this 3 V battery? Is it 500 mA hr at 3 V? (The energy conservation
> principle is telling me that yes it is 500 mA hr at 3 V, but I just want
> to be sure)

Batteries in series add voltage, batteries in parallel add capacity

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