$$4\frac{x-5}{3}=\frac{x-3}{5}$$
$x = \frac{91}{17} = 5\frac{6}{17} \approx 5.352941176$
$$20\left(x-5\right)=3\left(x-3\right)$$
$$20x-100=3\left(x-3\right)$$
$$20x-100=3x-9$$
$$20x-100-3x=-9$$
$$17x-100=-9$$
$$17x=-9+100$$
$$17x=91$$
$$x=\frac{91}{17}$$
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