Let $\lambda$ be the eigen value.
then,
$\begin{vmatrix} 2- \lambda &-1 \\ -4 & 5- \lambda \end{vmatrix}=0$
$\implies \lambda^2 -7 \lambda +10 -4 = 0$
$\implies \lambda^2 -7 \lambda +6 = 0$
If we substitute the options then only Option $C.$ will satisfy.
$\therefore$ Option $C.$ is the correct answer.