[techhelpbb]

My advice is a step-up switching regulator like in the FIRST PDB.
Going into a step-down switching regulator sort of like inside the cRIO.

National Semiconductor makes parts that will switch battery voltage up to roughly 20V.
Obviously because look at the cRIO input voltage.

National Semiconductor also makes parts that will switch roughly 20V down to 5V.

Each stage of regulation is both a noise filter and complements the other.

If you switch up to 20V and the battery caves to 8V the 20V suffers.
However the next stage just needs to get 5V so that 20V quality issue is damped.

Each stage will be probably about 87% to 95% efficient with switching regulation.

On the other hand a 7805 as pictured will remove the excess energy as heat.
If the battery is 14.3V depending on the current enough heat for a heatsink.
Sure you can get a TO3 metal can version of the 7805 or make an external pass transistor but it still just burns energy off as heat.
If you do build that 7805 circuit you should install blocking and bypass silicon diodes.