ZA-SAMO 2018 Problem 2

In a triangle $ABC$ , $AB = AC$ , and $D$ is on $BC$ . A point $E$ is chosen on $AC$ , and a point $F$ is chosen on $AB$ , such that $DE = DC$ and $DF = DB$ . It is given that $\frac{DC}{BD} = 2$ and $\frac{AF}{AE} = 5$ . Determine that value of $\frac{AB}{BC}$ .