If you're trying to get exactly 5V zener voltage, forget it. Zener voltage varies with current, and provided you are using a simple zener and resistor circuit, the output voltage will vary with input voltage. Also, most zeners are only available in +/-5% tolerances; a few are in +/-1%.
4.7V and 5.1V zeners are the closest standard +/-5% values.
If you want a voltage as close as possible to the 5 Volts, you could also use a TL431, adjustable zener.
With a couple of presision resistors you can make the TL431 to give 5 Volts.