You are right philipsi that for 5V you would use 5V zener.
Actually you will have to get whatever is closest match
to voltage you need. In this case that yould be zener
with 5.1V (I don't think anyone makes actual 5.0V zener).
You also need resistor in series with the zener. This is where
"excess" voltage is burnt. For example if you use 9V battery,
resistor will take the 4V while zener will maintain 5V.
Even as battery voltage drops to 7V, zener will keep the 5V
so resistor will drop only 2V (2+5=7).
Such circuit would not be very usefull without load. But when
you add load, it is not hard to bring zener circuit out of balance.
Zener is usually used in fairly narrow range so if you plan to
power some circuit using zener as regulator and you experience
difficulties, you can always return to voltage regulator chips such
as famous LM340 or 7805. They provide not only better regulation
and in wider operating range, they will waste less power than
zener circuit (might be important if you plan on using batteries).