Math Snap

STEP 1

1. The circle has a radius of $5$.
2. The angle intercepting the arc measures $\frac{\pi}{6}$ radians.
3. We need to find the length of the arc.

STEP 2

1. Recall the formula for the arc length.
2. Substitute the given values.
3. Calculate the arc length.

STEP 3

Recall the formula for the arc length:
$$\text{Arc Length} = \theta \times r$$ where $\theta$ is the angle in radians and $r$ is the radius of the circle.

STEP 4

Substitute the given values into the formula:
$$\text{Arc Length} = \frac{\pi}{6} \times 5$$

Calculate the product:
$$\text{Arc Length} = \frac{\pi}{6} \times 5$$ $$= \frac{5\pi}{6}$$ The length of the arc is:
$$\boxed{\frac{5\pi}{6}}$$