#### Answer

$x=-22$

#### Work Step by Step

Using cross-multiplication and the properties of equality, the value of the variable that satisfies the given equation, $
\dfrac{x+2}{4}=\dfrac{x-3}{5}
,$ is
\begin{array}{l}\require{cancel}
5(x+2)=4(x-3)
\\\\
5x+10=4x-12
\\\\
5x-4x=-12-10
.\\\\
x=-22
\end{array}