The 5 days thing is due to it being 10 days since the contact with the person who has coronavirus, which was 5 days before they were pinged (I think).
Apparently, no tests negate the need to self-isolate, however I’ve heard anecdotal tales of the phone T&T service saying otherwise?
If by pinged you mean on the app, it’s only advisory – so in essence do what you want legally. Morally speaking it’s a choice for you to make, in your situation I’d be cracking on.
RM.