Extracting the best X-KM segment within runs, and compare with other runs.

I would like to see if there is a way to extract the best 5 KM for any run activity, no matter if it was 10km or 5km.

One way is to simply use the native ">‑3">capability of the fēnix‑3 to determine the best 5km stretch on any tracked run that covers at least 5km, which the device uses to check whether you have achieved a new personal record for that distance. You can repurpose it by clearing the 5km personal record on your watch only before a run, so that the best 5km time over the course your next run will automatically get reported as a new personal record.

It isn't going to interfere with your historical 5km personal record as captured in your Garmin Connect account. If you manage to do better than it, then Garmin Connect will recognise it upon syncing with your watch and update your account accordingly; if you don't, then Garmin Connect will simply reject what your watch advises as a new personal record.

Obviously, this only works once for each run, without it being captured as part of the run activity record created by your watch.

…I feel that I might be doing good on a segment of 5km within that 10km run, but I dont know how to visualize it.

That's a different thing again. Telling you the best 5km time does not imply telling you over which 5km specifically; it's just a scalar number without any other dimension or metadata.

Specially if I would like to compare the best 5 km on any race I did in a month, or so.

You can't do that with capabilities provided by Garmin either on your watch or in Garmin Connect. I'm not sure whether you can develop and/or commission and install a Connect‑IQ app to use instead of a factory-installed Run activity profile (or ‘app’), such that it will write the best 5km time into the each FIT file it records, but even if that is possible, comparing that numeric attribute across selected (manually, or by search criteria such as date span) activity records will be a challenge.

…

I'm pretty sure I've seen someone post a screenshot on here, a few months back, of something that lays the elapsed time of a run on a straight line, with multiple bars above it indicate which parts yielded the best 1km and 5km times, etc. I spent fifteen minutes just now searching for it but couldn't find it, though, so I don't know if it was MapMyRun, Runkeeper, Strava or something else. Oh well.

I think I get some of what you are looking for...

the best way I have done things like that - is on some of my common running routes I created segments/courses in Garmin/MapMyRun/Strava - this allows for me to view "My efforts" and show my history (including pace, heart rate, date, etc). I have done various segments as half mile or 1km....then 1mi....or 3.1mi - or whatever a good segment might be. I make mental note of these spots/courses when I am out running or biking on a 'workout' day - whether it is a Tempo, Intervals, or one off sprint-surges etc..... easy to look back on that way.

Otherwise just have to course though lap data on your own... from various workouts.

Strava compares runs you commonly do automatically which is neat also.

Garmin - Strava - MMR - etc - all have some strengths in how they handle data, PR's , history graphs, segments. Plus its a good way to 'backup' your data.

I remember see on DCRAINMAKER.COM where he used software or website that allowed you to break the data down into laps of any size. By playing with different laps sizes and look at the speed/pace on them you could probably pick out the fasted.

SportTracks can sort of do what you want. It allows you to track your fastest 1km, 5km, etc over time. It will show you when you set a new time and will show you the segment of the run that you set it.

It's a paid site, about $US60 per year.

EDIT:

Golden Cheetah can do what you want, in that it will show you the fastest 5km segment of a run. You can produce a chart and show the segment trend over time.

It is also possible to pick put the fastest 5km segment from a run which you can then see on the map where it was.

It's a free download. You download the program and it works standalone on your computer. It has a bit of a learning curve though.

SportTracks can sort of do what you want. It allows you to track your fastest 1km, 5km, etc over time. It will show you when you set a new time and will show you the segment of the run that you set it.

It's a paid site, about $US60 per year.

EDIT:

Golden Cheetah can do what you want, in that it will show you the fastest 5km segment of a run. You can produce a chart and show the segment trend over time.

It is also possible to pick put the fastest 5km segment from a run which you can then see on the map where it was.

It's a free download. You download the program and it works standalone on your computer. It has a bit of a learning curve though.

I wouldn't mind paying the $60 a year,, but I will try Golden Cheetah this week.
Thanks a lot for the suggestion.