I don't think it is a mistake. I suspect that this could be a US/GB difference, but I think it is fine to say 'Her son is five; he is not at school yet.'. In fact, for me, this would the more natural way to say this. If the child is too young to attend school, he is not 'at school yet'. This mother might say 'I've got three children - one at secondary school, one at primary school and one who isn't at school yet'. Speakers of US English tend to say 'in school', 'in college' and so on, whereas speakers of British English say 'at school' 'at university', and so on, to refer to a person's stage of education. There aren't many difference in preposition use between US and GB English, but this seems to be one of them.