Garmin Connect should auto-detect your PR for activities that meet the requirements described on the Personal Records widget on your Dashboard. You can see this if you click the little help icon, which looks like a blue circle with a question mark, on the Personal Records widget. Here is a screen capture...
So, Garmin Connect won't process Personal Records that occur as part of a longer activity. i.e., if you run for a total of 5 miles, and you set a 5K Personal Record during that run, Garmin Connect won't recognize that as a PR. It does not matter if you press Lap at the start and end of your 5K, and the lap length is exactly 5K. The entire activity has to be 5K. This means that you have to start a new activity at the start of your 5K, and you have to save the activity (by pressing Stop and then holding down the Lap button) with a total distance of approximately 5K.
Some of the information I have been reading seems to indicate that they are trying to add segment support. If this segment stuff is going to do what I think it is, then this limitation may go away in the future.
