Not sure whether it was available 4 years ago, but you actually can view your best performances for 5k, 10k (or whatever else distance) pretty easily in Garmin Connect. Although it is not perfect and not exactly what you wanted, it can help you:
You could also set the maximum distance, if you know no 5k records were done at distance longer than the upper limit. Although the results won't show you directly the best times for exactly 5km (the runs are typically longer), it can help you seeing the fastest runs for given distance.
Another possibility is tagging each activity when you create the new PR - either by using the "favorite" flag (a star), or by selecting one of the available "Event Type" options, or simply by adding a tag directly at the beginning of the activity title (i.e. "[PR5k] Morning Run"). You can then filter your runs by that tag. And you can also add the exact 5km PR time into the notes, so that you can see it in future, when you list your PR's again. You could even put the time into the title too - it would allow you to sort by it, and see it directly in the table. For example "[PR5k 24:28] Morning Run", "[PR5k 24:56] Sunday Run", etc.
And then, yet another possibility that is quite useful (though also not exactly what you asked for), is the use of Segments.If you run frequently through the same paths, you can create segments on the path (of any number, and any distance you wish), and then whenever you run through the same segment, you'll see you ranking and a chart with all your previous runs in it.