It's so like my parents!
My mum is just like that - I asked her when I learned to swim as I knew it was just before I went to school, and she said 'oh you were 3' (just about possible) - 'you had done your mile (1500m) before you went into reception......'
Now I know this to be total rubbish, firstly if I had done a 1500m badge (64 lengths!) BEFORE I WAS 5 then something has gone wrong, because I should presumably be an Olympic cross-channel or even cross-ocean swimmer by now. But actually I can remember doing that badge, and it was just before I left primary school when I was 10! Which is slightly different...and ever so slightly less impressive....