1997 Cayley Problem 24

In a convex polygon, exactly five of the interior angles are obtuse. The largest possible number of sides for this polygon is

\textbf{(A)}\ 7\quad \textbf{(B)}\ 8\quad \textbf{(C)}\ 9\quad \textbf{(D)}\ 10\quad \textbf{(E)}\ 11

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.