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