(2) - Outcoming

In triangle $\text{ABC}$ with $\text{AB} = 5$ and $\text{AC} = 7$ .
$\text{D}$ is a point on line segment $\text{CA}$ such that $\text{CD} = 5$ .
$\text{E}$ is a point on line segment $\text{BA}$ extended such that $\text{AE} = 2$ .
If $\text{BC} = 8$ then $\text{AF} = \sqrt{\dfrac{a}{b}}$ , with $(a, b) = 1$ . What is the value of $a + b$ ?