Op, you sound like an amazing mum.
He cannot force you to continue with the current contact since the drop off has changed. I appreciate you can't afford legal costs but you can send an email as BusyLizzie61 suggested.
Start by saying you fully support daughters relationship with him and have for X years followed the agreement on current drop off location however as he notified you xx days ago (mention the date) of his impending move the current order will no longer apply and you'll both need to consider logistics. Given your daughters age her wishes and feelings should be taken into account and she does not want to travel 10 hours EOW for contact.
You can ask him for his suggestions and state that as he has given short notice of the move perhaps for this contact (mention date) that he visit her locally. This would enable continuity of contact whilst trying to resolve a longer term plan.
You could also mention that if this isn't suitable you are happy to adhere to the current schedule and meet as usual on Friday as per the contact arrangement.
State that as his residence has changed from X to Y a review of contact will be needed. Reiterate that your daughters preference is to not drive to the new location but for him to visit locally and you hope that he can accommodate her wishes and feelings.
As long as you offer contact you are not going to be seen by a court as causing an issue, especially if you have done this religiously for years.
He can either bully you into driving more, agree a more sensible schedule or apply to court to vary the order. That's all he can do. I know it's scary standing up to these entitled men but stick with it. Don't start doing the 5 hours unless a court forces you (they wouldn't!)
You could apply yourself to court. There is a form you complete and pay an amount. If you phoned your local family court they would be able to advise you. This would kick off the process and he can't say you are not supporting contact. There are delays which will work in your favour!
Keep offering local contact or to adhere to the current schedule. I would be wary of offering once a month as this may even be too onerous. A court HAS to take the safety of long distance driving into account especially if it impacts your rest or work. She could show that Sunday afternoons are your recovery time, you don't need to be specific but state the times you would be available on a Friday or Sunday to drop off/collect.
Bolster your daughters confidence by telling her she does have a voice and that she can choose to reduce contact if that works best for her. A cafcass officer WILL listen to her. She may feel sad about losing time with her half sibling and Dad but that isn't her fault and she can still stay in contact via video and holidays. Just reassure her that as she gets older her parents have to listen to her and in 5 years she will be an adult so can make her own decisions. This process is a step on that road to adulthood.
Don't put yourself and your daughter through 5 hours each way for a weekend. It really isn't safe or sensible. Trust yourself on this and it will come good.