AHSME 1960 Problem 16

In the numeration system with base $5$, counting is as follows: $1, 2, 3, 4, 10, 11, 12, 13, 14, 20,\ldots$. The number whose description in the decimal system is $69$, when described in the base $5$ system, is a number with: $\textbf{(A)}\ \text{two consecutive digits} \textbf{(B)}\ \text{two non-consecutive digits} \\ \textbf{(C)}\ \text{three consecutive digits} \textbf{(D)}\ \text{three non-consecutive digits} \\ \textbf{(E)}\ \text{four digits}$