Answer
$\dfrac{2x+16}{(x+2)(x+2)(x-2)}$
Work Step by Step
Factoring the given expression, $
\dfrac{5}{x^2-4}-\dfrac{3}{x^2+4x+4}
,$ results to
\begin{array}{l}
\dfrac{5}{(x+2)(x-2)}-\dfrac{3}{(x+2)(x+2)}
.\end{array}
Using the $LCD=
(x+2)(x+2)(x-2)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{(x+2)(5)-(x-2)(3)}{(x+2)(x+2)(x-2)}
\\\\=
\dfrac{5x+10-3x+6}{(x+2)(x+2)(x-2)}
\\\\=
\dfrac{2x+16}{(x+2)(x+2)(x-2)}
.\end{array}
