Answer
$C \approx23.2^\circ$;
$B \approx56.8^\circ$;
$b \approx4.25$
Work Step by Step
Step 1. Use the Law of Sines: $\frac{2}{sinC}=\frac{5}{sin100^\circ}$, thus $C=sin^{-1}(\frac{2sin100^\circ}{5})\approx23.2^\circ$
Step 2. $B=180-A-C\approx56.8^\circ$;
Step 3. $\frac{b}{sin56.8^\circ}=\frac{5}{sin100^\circ}$, thus $b=\frac{5sin56.8^\circ}{sin100^\circ}\approx4.25$
