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>Find the perimeter of the given triangle $\triangle D E F,$ if $\triangle A B C \sim \triangle D E F, A B=5$, $B C=6, A C=7,$ and $D E=3$