Answer
$\dfrac{(x+5)(x+4)}{3}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, the given expression, $
\dfrac{x^2-25}{3}\div \dfrac{x^2-10x+25}{x^2-x-20}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^2-25}{3}\cdot \dfrac{x^2-x-20}{x^2-10x+25}
\\\\=
\dfrac{(x+5)(x-5)}{3}\cdot \dfrac{(x-5)(x+4)}{(x-5)(x-5)}
\\\\=
\dfrac{(x+5)(\cancel{x-5})}{3}\cdot \dfrac{(\cancel{x-5})(x+4)}{(\cancel{x-5})(\cancel{x-5})}
\\\\=
\dfrac{(x+5)(x+4)}{3}
.\end{array}
