$$\frac{n}{2}+\frac{n}{3}-\frac{1}{2}=\frac{n}{5}+\frac{1}{3}$$
$n = \frac{25}{19} = 1\frac{6}{19} \approx 1.315789474$
$$15n+10n-15=6n+10$$
$$25n-15=6n+10$$
$$25n-15-6n=10$$
$$19n-15=10$$
$$19n=10+15$$
$$19n=25$$
$$n=\frac{25}{19}$$
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