smc

The probability of rolling at least a five on any one roll is $\frac{2}{6}=\frac{1}{3}$. If there are exactly $5$ fives or sixes rolled, there are $\left(\genfrac{}{}{0ex}{}{6}{5}\right)=6$ ways to pick which of the rolls are the fives and sixes, and so the probability in this case is $6{\left(\frac{1}{3}\right)}^5\left(\frac{2}{3}\right)=\frac{12}{729}$. If there are exactly $6$ fives or sixes rolled, then there is only one way to pick which of the rolls are fives and sixes, so the probability in this case is ${\left(\frac{1}{3}\right)}^6=\frac{1}{729}$. Therefore, the total probability is $\frac{12}{729}+\frac{1}{729}=\frac{13}{729},\boxed{\frac{13}{729}}$.