Final answer:
There are 3125 different ways to press 5 buttons when repetition is allowed, calculated as 5 to the power of 5.
Step-by-step explanation:
To calculate the number of different ways there are of pressing 5 buttons where repetition is allowed, we use the principle that the number of possible outcomes (or microstates) of any repeated independent event is equal to the number of possibilities for one event, raised to the power of the number of repetitions.
If there are 5 buttons to choose from for each press, and you're pressing buttons 5 times, the formula becomes 55.
This calculation would then be 5 x 5 x 5 x 5 x 5 which equals 3125.
Therefore, there are 3125 different ways to press the buttons.