To determine how many miles the whale swims each day, we can divide the total distance by the number of days:
\[ \text{Miles per day} = \frac{200 \text{ miles}}{5 \text{ days}} = 40 \text{ miles per day} \]
Now, to find out how many miles the whale will swim in 16 days, we multiply the daily distance by the number of days:
\[ \text{Total miles in 16 days} = 40 \text{ miles per day} \times 16 \text{ days} = 640 \text{ miles} \]
Therefore, the whale will swim 640 miles in 16 days.