2018 Cayley Problem 16

A ladder has 5 rungs. Elisabeth can climb up by 1 or 2 rungs at a time. In how many different ways can she climb up to the fifth rung of the ladder?

\textbf{(A)}\ 10\quad \textbf{(B)}\ 9\quad \textbf{(C)}\ 7\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 8

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.