1986 AHSME Problem 23

Let N = 69^{5} + 5 \cdot 69^{4} + 10 \cdot 69^{3} + 10 \cdot 69^{2} + 5 \cdot 69 + 1. How many positive integers are factors of N?

\textbf{(A)}\ 3\qquad \textbf{(B)}\ 5\qquad \textbf{(C)}\ 69\qquad \textbf{(D)}\ 125\qquad \textbf{(E)}\ 216

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