I would think that because your child lives elsewhere for 5 days (with mum I assume) that person would be the one who would be rightfully claiming the CB but of you want to be certain just phone CB helpline and ask them.
My ex is getting the child element on her benefits, but she doesn’t have custody, and our child lives with me full time. When we were in court going through the custody, she was actually ordered to pay it to me (though she didn’t), and when I questioned my solicitor if she should still be getting it, he said the requirement to be entitled was very low. It seems a child doesn’t even need to stay overnight, you just need to have some of the child’s stuff at your home in order to be entitled to it.
Definitely worth giving the benefits office a call just to query it and they may just need to upload a birth certificate.