Answer
$x=6$
Work Step by Step
First, the solutions must satisfy $\left\{\begin{array}{l}
x+4\gt 0\\
x-4\gt 0
\end{array}\right.\quad \Rightarrow x\gt 4\qquad (*)$
in order for the equation to be defined.
On the RHS, apply$ \quad\log_{a}(MN)=\log_{a}M+\log_{a}N$
$\log_{5}[(x+4)(x-4)]=\log_{5}20$
... apply the principle of logarithmic equality
$(x+4)(x-4)=20$
$x^{2}-16=20$
$x^{2}=36$
Possible solutions:
$ x=-6\qquad$... does not satisfy (*), not a solution.
$x=6\qquad $... satisfies (*), and is a valid solution.
