Answer
Solution set = $\{-19\}$
Work Step by Step
Multiply both sides with the LCD, $24$
$ 24 \left[5+\displaystyle \frac{x-2}{3}\right]=24 \left[ \dfrac{x+3}{8} \right]\quad$ ... distribute and simplify
$ 120+4(x-2)=3(x+3)\quad$ ... distribute and simplify
$120+8x-16=3x+9$
$ 8x+104=3x+9\quad$ ... add $-3x-104$ to both sides
$8x-3x=9-104$
$5x=-95$
$x=-19$
Solution set = $\{-19\}$
