How to power an Arduino Uno with 3 1.5V batteries?
The Arduino doesn't require 5V.

The Atmel chip on the board requires somewhere between 1.8V and 5.5V, the Arduino just happens to have chosen 5V as a good common widely used voltage to run at.

If you provide a voltage within that range to the +5V pin the board will operate.  There's a couple of caveats though:


Anything below about 4V will mean the 3.3V regulator won't be working right, so the 3.3V pin won't be functioning properly
At lower voltages the Atmel chip can't operate reliably at higher frequencies, which is why 3.3V Arduino boards operate at 8MHz instead of 16Mhz.


So 3 x AA batteries is a perfect power source for running the Arduino, direct into the 5V pin.  Just make sure that you don't power it any other way at the same time or you'll be pumping 5V into your batteries.  You may want to add a Schottky diode in series with your battery + (between battery + and the 5V pin) to stop that ever causing a problem.  Choose one with a very low forward voltage drop though, otherwise you could end up dropping too much of your precious voltage over the diode.

By the way, when you're powering it from USB the 5V could be anywhere between 4.75V and 5.25V.