$\frac{5}{x+2} - \frac{2x-1}{5} = 0$

$\frac{5}{x+2} - \frac{2x-1}{5} = 0$
Multiply both sides by the common denominator and then make some order and then multiply both sides by $-1$:
$25-2x^2-3x+2=0\,\Longrightarrow\,2x^2+3x-27=0$
$x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ....I think the solutions are $-4.5\,,\,\,3$ , but check this carefully.