It's in relation to a run, though - what else could it mean but distance? Steps? Maybe, but I've genuinely never heard of that being used as a goal when running. Seconds? Again, it's a possibility, but it'd be more usual to say something like "1h23-ish" - and, besides, that'd be a really odd time to pick.

And even in the UK, where many people still measure longer distances in miles, I've never heard anyone talk about a run being however many thousand feet or yards or chains or whatever.

All of the first page results for a USA-based google search for "5k" are running-related too, so it can't really be all that ambiguous there either.