1974 AHSME Problem 24

A fair die is rolled six times. The probability of rolling at least a five at least five times is

\mathrm{(A)\ } \frac{13}{729} \qquad \mathrm{(B) \ }\frac{12}{729} \qquad \mathrm{(C) \ } \frac{2}{729} \qquad \mathrm{(D) \ } \frac{3}{729} \qquad \mathrm{(E) \ }\text{none of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.