Answer
$C= 165^\circ$
$a \approx3.35$
$c\approx1.68$
Work Step by Step
Step 1. Using the given figure and conditions, we have $C=180-10-5=165^\circ$
Step 2. Using the Law of Sines, we have $\frac{a}{sin10^\circ}=\frac{b}{sin5^\circ}=\frac{5}{sin165^\circ}$
Step 3. Thus $a=\frac{5sin10^\circ}{sin165^\circ}\approx3.35$ and $c=\frac{5sin5^\circ}{sin165^\circ}\approx1.68$
