AMC 12 2018a Problem 5

What is the sum of all possible values of $k$ for which the polynomials $x^2 - 3x + 2$ and $x^2 - 5x + k$ have a root in common?

$\textbf{(A) }3 \textbf{(B) }4 \textbf{(C) }5 \textbf{(D) }6 \textbf{(E) }10$