2018 AMC 8 Problem 14

Let N be the greatest five-digit number whose digits have a product of 120. What is the sum of the digits of N?

\textbf{(A) }15\qquad\textbf{(B) }16\qquad\textbf{(C) }17 \qquad\textbf{(D) }18\qquad\textbf{(E) }20

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