To find the length of the arc (L) formed by a central angle in a circle, we can use the formula:
\[ L = r \times \theta \]
where \( r \) is the radius and \( \theta \) is the central angle in radians.
Given:
- \( r = 30 \) inches
- \( \theta = \frac{5\pi}{3} \) radians
Now we can substitute these values into the formula:
\[ L = 30 \times \frac{5\pi}{3} \]
Calculating this:
\[ L = 30 \times \frac{5\pi}{3} = \frac{150\pi}{3} = 50\pi \]
Thus, the length of the arc is:
\[ \boxed{50\pi} \]