How the fuck would the dog burn the carpet? Are you sure they just didn't wanna scold you for whatever reasons? You'll usually notice when a 5 year old is lying. :D
My mom told me that I admitted to her (being 12 back then) that I knew that she was the Nikolaus (old tradition, Nikolaus puts sweets and fruit in your polished shoes the night of the 6th december) but I still imagined that even though I was fast asleep, she'd dress up as Nikolaus to put the sweets in my boots.
My parents believed me.
And I know they believed me because my parents aren't like that. If I did something and lied about it, they would keep pestering me.