today I run five km. But connect don’t update the record like Strava.
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Garmin Connect does not perform post-processing to scan each uploaded activity record for the fastest one-kilometre stretch, one-mile stretch, five-kilometre stretch, etc. within the total distance that was run. If the total distance matches one of the predetermined distances for which personal records are tracked, it may look at the 'timer' in the activity record, to determine if a new personal record has been achieved. In your example, 32'37.1" is not faster than 32'17", which is your 5-km personal record as far as Garmin Connect is concerned; therefore, whether 5.04km qualifies as being close enough to 5km would be an irrelevant question.