The values are given, $R=50 \mathrm{\Omega }$, $\epsilon =5 \mathrm{V}$, $i=50\times {10}^{-3} \mathrm{A}$ and $t=0.1 \mathrm{s}$, the equation of, 
 $$\begin{gathered} i=i_0\left(1-e^{-\frac{t\times R}{L}}\right) \\ \Rightarrow 50\times {10}^{-3}=i_0\left(1-e^{-\frac{0.1\times 50}{L}}\right) \end{gathered}$$

Now use the relation between current and voltage, $i_0=\frac{\epsilon }{R}=\frac{5}{50}$, 

it means, 
$$\begin{gathered} \Rightarrow 50\times {10}^{-3}=\frac{5}{50}\left(1-e^{-\frac{0.1\times 50}{L}}\right) \\ \Rightarrow 50\times {10}^{-2}=\left(1-e^{-\frac{0.1\times 50}{L}}\right) \\ \Rightarrow L=\frac{5}{\ln 2} \end{gathered}$$