Nice. The reason I said to take the 5 output volts and put it on the VIN pin is- that the Arduino's voltage regulator will not do anything as it's already 5 volts.
If you're putting power through it, why would you presume it would do nothing?
Am I mistaken?
Quite. There are a couple of issues with this. Firstly, in this scenario where you're chasing every ounce of efficiency there's a loss to the operation of the regulator, even if it doesn't need to divert excess power to heat. The cost of running (or quiescent current) for a common L7805 5V regulator is 6mA, according to table 4 of the datasheet (link to datasheet
) or, more than 1/10th your project's total power consumption as calculated by CrossRoads earlier in this thread.
Also a linear regulator requires a particular minimum voltage in order to guarantee the desired regulated output. In the case of that same example linked above, this minimum is 2V above the regulated output voltage, or 7V. If you google 'dropout voltage' you'll find examples where 5V input will deliver 4.9V approx output (for the 7805 regulator linked above) and get a better explanation of what this means.
Bottom line is there's no need to regulate your input voltage twice, and if you're wanting maximum life out of this battery set-up it's best to power only the components you actually need.