555 timer - Creating a 5 second astable pulse
There are at least three things that can affect this:


Tolerance of the components. Your resistors and capacitors may be +/- 10% or more.
Tolerance in voltage of the 555 -- what is the actual VCC and the actual threshold voltage?
Variation based on temperature or other ambient conditions.


If you are within spitting distance of the timing you need, slightly adjust the capacitor or resistors until you get where you need to be. Easiest would be to perhaps use a potentiometer to make those adjustments.

And I agree with everyone else: In real life, it's easier to use a microcontroller with built-in timers and oscillators. An AVR ATTiny85 would need zero support components to do this (although a de-coupling capacitor would be good form.) Too bad you can't use it :-)