Also, don't forget that a 5K is actually 3.1 miles. So when you motor through two miles in a certain time, remember that you not only have one more mile to go, but also another 10th of a mile, or about 40 to 50 more seconds.
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In many cases, the key to running faster can be found in subtly changing your training regimen, not your racing strategy. If you're slowing down in the third mile, you may need to increase your tolerance to lactic-acid buildup. (Lactic acid from your working muscles can make you feel stiff and "dead-legged" at the end of a hard effort.)
This workout should help:
Run a two-mile warmup jog, followed by two miles of tempo running at 15 to 20 seconds per mile slower than your 5K goal pace. Then, after three to five minutes of easy jogging for recovery, run one mile at your 5K race pace (this would be about 5:15 to 5:20 based on your PR of 16:32). Next, jog a half-mile to recover. Then run a half-mile at slightly faster than 5K race pace (around 2:35). Finish the session with a two-mile cool down.
This workout teaches your mind and body to hold a hard-but-steady pace even when you're a bit tired (as you will be by the third mile of the race). Try this every 10 days or so. If it becomes relatively easy, add another half-mile repeat to the end of the workout.