2017 Cayley Problem 19

Two lines with slopes \frac{1}{4} and \frac{5}{4} intersect at (1,1). What is the area of the triangle formed by these two lines and the vertical line x = 5?

\textbf{(A)}\ 5\quad \textbf{(B)}\ 10\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 12\quad \textbf{(E)}\ 15

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.