To find the probability of rolling a 5 on a single die twice, we first determine the probability of rolling a 5 on one roll of a die.
When rolling a standard six-sided die, there are 6 possible outcomes: 1, 2, 3, 4, 5, and 6. The probability of rolling a 5 on one roll is:
\[ P(\text{rolling a 5}) = \frac{1}{6} \]
Since the rolls are independent events, the probability of rolling a 5 on both the first and the second roll is the product of the probabilities of each individual roll. Thus, we have:
\[ P(\text{rolling a 5 on first roll and a 5 on second roll}) = P(\text{rolling a 5 on first roll}) \times P(\text{rolling a 5 on second roll}) \]
Substituting the probabilities:
\[ P(\text{5 on first roll and 5 on second roll}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \]
Therefore, the probability of getting a 5 the first time and a 5 the second time is:
\[ \frac{1}{36} \]