I think testing is a great idea MJK. You sound really frustrated and it can help provide answers. Do you think your daughter would cooperate with the tester?
I am not an expert but several on this board know quite a lot about testing and child behavior. I wanted to give your situation a bump and see if you can get someone who knows more to ring in.
You also might want to post the same info again with a different title in "Parenting & Advocacy". Maybe something like "DD5 going underground already! Help!" "Going underground" is the term for girls hiding their intelligence to fit in but they usually wait until teens to do this. Your DD clearly has something else going on because she does it at home too.
I hope you get some replies.