It's really bad that your ds was being told to falsify work. That doesn't give him a good message. I don't understand what this "work" was, however: home educated kids in the UK don't have to show "work" to anyone (except possibly their own parents if the parents want to see it).
Aside from that, I am not at all convinced that your son's stint of home education was a total disaster. Things at school must have been very bad indeed for him to have been expelled. Would he be on track to get more than 5 GCSEs if he had gone to the PRU? Maybe, maybe not. Perhaps his academic attainment would have been worse at the PRU than it now is. Nobody can say.
What's wrong with 5 GCSEs? That's perfectly respectable. It isn't true that he only has a chance to do five. Better to tackle five now than to hate school so much he starts school refusing or finds a way to get himself expelled from the current school too. If he wants to do more academics later, he can.
It will only be "too late" for that if your son has got the message that learning only happens under duress and before the age of 16, and that kids who don't get ten good GCSEs in Y11 are failures. I hope he hasn't heard you saying how disappointed you are. If he takes on board your idea that he's all washed up already, will he see any point in applying himself to achieve these five exams or do something else worthwhile with his life?
Your lad has been going through a very rough time in his education and family life, with lots of upheaval. Be proud of what he is managing to do now. Don't let him know that you think his best isn't good enough.