Final answer:
The probability of being in state 5 in the long run for an ergodic 5-state system is 0.2. This is because all microstates are equally probable.
Step-by-step explanation:
An ergodic system refers to a system where every microstate is equally probable. In the case of a 5-state system, there are a total of 5 macrostates or possible states. To find the probability of being in state 5 in the long run, we need to determine the proportion of microstates that correspond to state 5.
Based on the provided information, it is equally probable to get 5 heads as it is to get 5 tails when tossing 5 coins. Therefore, the probability of being in state 5 in the long run is 0.2.