Answer
$C \approx23.2^\circ$
$B\approx 56.8^\circ$
$b \approx4.25$
Work Step by Step
1. Use the Law of Sines $\frac{5}{sin100^\circ}=\frac{2}{sinC}=\frac{b}{sinB}$
2. Thus $C=sin^{-1}(\frac{2sin100^\circ}{5})\approx23.2^\circ$
3. Find the third angle $B\approx180-100-23.2=56.8^\circ$
4. $b=\frac{5sin56.8^\circ}{sin100^\circ}\approx4.25$
