$$5^{m}\div5^{-3}=5^{5}$$
$m=2$
$$125\times 5^{m}=3125$$
$$5^{m}=25$$
$$\log(5^{m})=\log(25)$$
$$m\log(5)=\log(25)$$
$$m=\frac{\log(25)}{\log(5)}$$
$$m=\log_{5}\left(25\right)$$
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