Why is 5.1V the standard Zener voltage and not 5V?
Zener diode voltages largely follow the E24 resistor value intervals, a range of a intervals specified with +/-5 % accuracy.

Zener diodes have not particularly developed as a technology, with accurate voltage references using bandgap techniques instead. The intervals have stayed the same for many years.

As an aside, Zener diodes are less commonplace in circuits than may be expected to electronics newcomers, who can sometimes regard them as appealing 'magic voltage drops'. Their combination of basic inaccuracy, notable variance with temperature and current and a fairly large working current for stability lessens their usefulness compared to other design approaches and components.