What is the probability that Shironda rolls a 5 on the number cube and then chooses a 5 from the deck?

$\frac{1}{78}$
The probability that one rows a 5 on a standard six-sided cube is $\frac{1}{6}$ since there is $1$ number on the dice that has the number 5 out of a total of 6 possibilities.
On a deck of 52 cards, there are four 5's (for each suit). Thus, the probability is $\frac{4}{52} = \frac{1}{13}$.
These events are independent. Thus, to calculate their P(A and B), we multiply their probabilities. $\frac{1}{6} \cdot \frac{1}{13} = \frac{1}{78}$.