Answer
$-\dfrac{37}{18}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the order of operations (PEMDAS - Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction) to simplify the given expression, $
\left(-\dfrac{5}{9}-\dfrac{2}{3}\right)-\dfrac{5}{6}
.$
$\bf{\text{Solution Details:}}$
Simplifying the expression/s in parenthesis by making the fractions similar (same denominator), the entire expression above becomes
\begin{array}{l}\require{cancel}
\left(-\dfrac{5}{9}-\dfrac{2}{3}\cdot\dfrac{3}{3}\right)-\dfrac{5}{6}
\\\\=
\left(-\dfrac{5}{9}-\dfrac{6}{9}\right)-\dfrac{5}{6}
\\\\=
\left(\dfrac{-5-6}{9}\right)-\dfrac{5}{6}
\\\\=
\left(\dfrac{-11}{9}\right)-\dfrac{5}{6}
\\\\=
\dfrac{-11}{9}-\dfrac{5}{6}
.\end{array}
Simplifying the sum/difference by making the fractions similar, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{-11}{9}\cdot\dfrac{2}{2}-\dfrac{5}{6}\cdot\dfrac{3}{3}
\\\\=
\dfrac{-22}{18}-\dfrac{15}{18}
\\\\=
\dfrac{-22-15}{18}
\\\\=
\dfrac{-37}{18}
\\\\=
-\dfrac{37}{18}
.\end{array}
