#### Answer

$s=20$ inches

#### Work Step by Step

Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$.
Step 2: $A=\frac{1}{2}r^{2}\theta=\frac{1}{2}\times r\times (r\times\theta)=\frac{1}{2}\times r\times s$
Step 3: Substituting values into the equation, $50=\frac{1}{2}\times5\times s$
Step 4: Simplifying, $50=\frac{5s}{2}$
Step 5: Multiplying both sides by \frac{2}{5},
$50\times\frac{2}{5}=\frac{5s}{2}\times\frac{2}{5}$
Step 6: Therefore, $s=20$ inches