Should I use an adjustable voltage regulator or a fixed voltage regulator?
As far as the efficiency is concerned, I would modify your question to: linear or switching voltage regulator? Both can be fixed or adjustable ..
If you need just 5V and you don't worry about power loses then the answer would be linear, fixed voltage regulator (for example, 7805 for 1A, for smaller currents 78L05, etc) ..
If you don't like converting to much power into heat, then the answer is switching regulator, and, as you need fixed 5V, fixed switching regulator will be the best choice, for example, LM2574-5V (1A), or hundreds of others of MAX-series, or LT-series or others ..
When will you select adjustable (linear or switching) voltage regulator: if you need adjustable output voltage, or, .. if you don't have fixed IC in hand ..
Regards,
IanP