AMC 8 2018 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 $N$? $\textbf{(A) }15 \textbf{(B) }16 \textbf{(C) }17 \textbf{(D) }18 \textbf{(E) }20$