$$\frac { m - 5 } { 2 } - \frac { m - 3 } { 5 } = \frac { 1 } { 2 }$$
$m=8$
$$5\left(m-5\right)-2\left(m-3\right)=5$$
$$5m-25-2\left(m-3\right)=5$$
$$5m-25-2m+6=5$$
$$3m-25+6=5$$
$$3m-19=5$$
$$3m=5+19$$
$$3m=24$$
$$m=\frac{24}{3}$$
$$m=8$$
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