To determine how far the runner can go in 16 minutes, we first need to calculate the runner's pace based on the initial information provided.
The runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes. The total distance of the race is 5 miles, so:
\[ \frac{1}{4} \text{ of 5 miles} = \frac{5}{4} \text{ miles} = 1.25 \text{ miles} \]
Since it takes 8 minutes to run 1.25 miles, we can find out how many miles the runner covers in 1 minute:
\[ \text{Miles per minute} = \frac{1.25 \text{ miles}}{8 \text{ minutes}} = 0.15625 \text{ miles per minute} \]
Now, to find out how far the runner can go in 16 minutes:
\[ \text{Distance in 16 minutes} = 0.15625 \text{ miles per minute} \times 16 \text{ minutes} = 2.5 \text{ miles} \]
Thus, the runner can go 2.5 miles in 16 minutes.
Therefore, the correct answer is \( \text{b) 2 1/2 miles} \).