2017 AMC 10B Problem 14

An integer N is selected at random in the range 1\leq N \leq 2020. What is the probability that the remainder when N^{16} is divided by 5 is 1?

\textbf{(A)}\ \frac{1}{5}\qquad\textbf{(B)}\ \frac{2}{5}\qquad\textbf{(C)}\ \frac{3}{5}\qquad\textbf{(D)}\ \frac{4}{5}\qquad\textbf{(E)}\ 1

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