Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 46

$x=\dfrac{2}{3}$

Multiplying both sides by the $LCD= 9 ,$ the value of the variable that satisfies the given equation, $ \dfrac{x-5}{3}+2=\dfrac{5}{9} ,$ is \begin{array}{l}\require{cancel} 3(x-5)+9(2)=1(5) \\\\ 3x-15+18=5 \\\\ 3x=5+15-18 \\\\ 3x=2 \\\\ x=\dfrac{2}{3} .\end{array}