AMC 12 2019b Problem 7

What is the sum of all real numbers $x$ for which the median of the numbers $4,6,8,17,$ and $x$ is equal to the mean of those five numbers?

$\textbf{(A) } -5 \textbf{(B) } 0 \textbf{(C) } 5 \textbf{(D) } \frac{15}{4} \textbf{(E) } \frac{35}{4}$