Answer
$m\approx 2.156$
Work Step by Step
$[1+\displaystyle \frac{m}{3}]^{5}=15\qquad \color{blue}{\text{ ... } /(...)^{1/5}}$
$[(1+\displaystyle \frac{m}{3})^{5}]^{1/5}=15^{1/5}$
$1+\displaystyle \frac{m}{3}=15^{1/5}\qquad \color{blue}{\text{ ... } /-1}$
$\displaystyle \frac{m}{3}=15^{1/5}-1\qquad \color{blue}{\text{ ... } /\times 3}$
$m=3(15^{1/5}-1)$
$m\approx 2.156$
