Answer
$-10$
Work Step by Step
Recall, in order to solve problems involving order of operations, we use the PEMDAS rule.
First Priority: P - parentheses and other grouping symbols (including fraction bars)
Second Priority: E - exponents
Third Priority: M/D - Multiplication or division, whichever comes first from the left to the right
Fourth Priority: A/S - Addition or subtraction, whichever comes first from the left to the right
We follow order of operations to obtain that the expression, $
\dfrac{4(-2-3)^2}{5}-\dfrac{5(-1-5)^2}{6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4(-5)^2}{5}-\dfrac{5(-6)^2}{6}
\\\\=
\dfrac{4(-5)(-5)}{5}-\dfrac{5(-6)(-6)}{6}
\\\\=
\dfrac{4(-\cancel{5})(-5)}{\cancel{5}}-\dfrac{5(-\cancel{6})(-6)}{\cancel{6}}
\\\\=
20-30
\\\\=
-10
.\end{array}
