I’m advocating not advertising.

I capitalise it out of muscle memory. That’s all. FWIW Wikipedia capitalises it as well.

I called it out with a link because I expect many folk to be unfamiliar with it, but the nature of parkrun itself — rather than simply going for a 5k[m] run — is intrinsic to the point I was trying to make.

5k is perfectly well understood to be a distance, especially in context, in British English and I’m a Brit. My bad I guess for not adding “m” for (some of) the HN readership. [EDIT: actually, I said 5km! Not my fault if parkrun says 5k, but they are a British organisation)

Regardless of that, you were correct that parkrun is indeed a run around a park. I won’t explain any further nor link anywhere lest it be misconstrued as advertising (something that’s proudly free, mind you). Besides which I need to get to and get my running kit on.