#### Answer

$\color{blue}{-\dfrac{37}{18}}$

#### Work Step by Step

Make the fractions similar by using their LCD of $18$ to obtain:
$=\left(-\dfrac{5(2)}{9(2)}-\dfrac{2(6)}{3(6)}\right)-\dfrac{5(3)}{6(3)}
\\=\left(-\dfrac{10}{18}-\dfrac{12}{18}\right)-\dfrac{15}{18}$
Simplify using the PEMDAS rule for order of operations. The PEMDAS rule summarizes the order of operations:
First Priority; P - parentheses
Second Priority: E - exponents
Third Priorirty: M/D - multiplication or division, whichever comes first from the left
Fourth Priority: A/S - addition or subtraction, whichever comes first from the left
Simplify within grouping symbols first::
$=\dfrac{-10-12}{18}-\dfrac{15}{18}
\\=\dfrac{-22}{18} - \dfrac{15}{18}$
Subtract to obtain:
$=\dfrac{-22-15}{18}
\\=\color{blue}{-\dfrac{37}{18}}$