In the given circuit (figure), current through the 5 mH inductor in steady state is

Inductors 5 mH and 10 mH are connected in parallel, hence

equivalent inductance $L_{\mathrm{eq}}=\frac{5\times 10}{5+10}=\frac{50}{15}=\frac{10}{3}\mathrm{mH}$

Current at steady state, $I=\frac{20}{5}=4\mathrm{A}$

As L₁ and L₂ are in Parallel

$I_1=I\left(\frac{L_2}{L_1+L_2}\right)=4\left[\frac{10}{10+5}\right]=\frac{8}{3}\mathrm{A}$