$$\frac{3x+5}{5}-\frac{x-2}{3}=\frac{5x-7}{6}$$
$x=5$
$$6\left(3x+5\right)-10\left(x-2\right)=5\left(5x-7\right)$$
$$18x+30-10\left(x-2\right)=5\left(5x-7\right)$$
$$18x+30-10x+20=5\left(5x-7\right)$$
$$8x+30+20=5\left(5x-7\right)$$
$$8x+50=5\left(5x-7\right)$$
$$8x+50=25x-35$$
$$8x+50-25x=-35$$
$$-17x+50=-35$$
$$-17x=-35-50$$
$$-17x=-85$$
$$x=\frac{-85}{-17}$$
$$x=5$$
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