$$\left. \begin{array} { l } { \frac { x - 5 } { 3 } = \frac { x - 3 } { 5 } } \end{array} \right.$$
$x=8$
$$5\left(x-5\right)=3\left(x-3\right)$$
$$5x-25=3\left(x-3\right)$$
$$5x-25=3x-9$$
$$5x-25-3x=-9$$
$$2x-25=-9$$
$$2x=-9+25$$
$$2x=16$$
$$x=\frac{16}{2}$$
$$x=8$$
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