$(1$ point$)$

Let $x(t)=\left[\begin{array}{c}{x}_1(t)\\ x_2(t)\end{array}\right]$ be a solution to the system of differential equations:

$x_1^{\text{'}}(t)=-5x_1(t)-6x_2(t)$

$x_2^{\text{'}}(t)=12x_1(t)+13x_2(t)$

$Ifx(0)=\left[\begin{array}{c}-5\end{array}\right]$

$-1,$ find $x(t).$

Put the eigenvalues in ascending order when you enter $x_1(t),x_2(t)$ below.