C

$\because DE$∥$BC$，
$\therefore \angle ADE=\angle B$.
$\because \angle ADE=\angle EFC$，
$\therefore \angle B=\angle EFC$，
$\therefore BD$∥$EF$，
$\because DE$∥$BF$，
$\therefore$四边形$BDEF$为平行四边形，
$\therefore DE=BF$.
$\because DE$∥$BC$，
$\therefore \triangle ADE$∽$\triangle ABC$，
$\therefore \frac{DE}{BC}=\frac{AD}{AB}=\frac{AD}{AD+BD}=\frac{5}{8}$，
$\therefore BC=\frac{8}{5}DE$，
$\therefore CF=BC-BF=\frac{3}{5}DE=6$，
$\therefore DE=10$.
故选：$C$.