#### Answer

$x=\dfrac{5}{2}\pm\dfrac{\sqrt{77}}{2}$

#### Work Step by Step

$x^{2}-13=5x$
Take the $5x$ to the left side of the equation:
$x^{2}-5x-13=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=-5$ and $c=-13$
Substitute:
$x=\dfrac{-(-5)\pm\sqrt{(-5)^{2}-4(1)(-13)}}{2(1)}=\dfrac{5\pm\sqrt{25+52}}{2}=...$
$...=\dfrac{5\pm\sqrt{77}}{2}=\dfrac{5}{2}\pm\dfrac{\sqrt{77}}{2}$