Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>In $\odot D, \overline{D E} \cong \overline{E C}, m \widehat{C F}=60,$ and
$\overline{D E} \perp \overline{E C} .$ Find $m \angle 5$