2024 AMC 12B Problem 6

The national debt of the United States is on track to reach 5 \cdot 10^{13} dollars by 2033. How many digits does this number of dollars have when written as a numeral in base 5? (The approximation of \log_{10} 5 as 0.7 is sufficient for this problem.)

\textbf{(A) }18 \qquad \textbf{(B) }20 \qquad \textbf{(C) }22 \qquad \textbf{(D) }24 \qquad \textbf{(E) }26 \qquad

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