$$\frac { x - 5 } { 3 } = \frac { x - 2 } { 5 }$$
$x = \frac{19}{2} = 9\frac{1}{2} = 9.5$
$$5\left(x-5\right)=3\left(x-2\right)$$
$$5x-25=3\left(x-2\right)$$
$$5x-25=3x-6$$
$$5x-25-3x=-6$$
$$2x-25=-6$$
$$2x=-6+25$$
$$2x=19$$
$$x=\frac{19}{2}$$
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