If the runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes, we can first determine the distance the runner covers in that time.
The total distance of the race is 5 miles, so:
\[ \text{Distance covered in 8 minutes} = \frac{1}{4} \times 5 \text{ miles} = 1.25 \text{ miles} \]
Next, we need to find out how far the runner can go in 16 minutes. Since 16 minutes is twice the time of 8 minutes, we can simply double the distance covered in 8 minutes:
\[ \text{Distance covered in 16 minutes} = 2 \times 1.25 \text{ miles} = 2.5 \text{ miles} \]
Thus, at the same pace, the runner can go 2.5 miles in 16 minutes.