I did my own and presented at the Land Registry. Pre-Covid of course.
The ID5 is what the legal/solicitor/conveyancer needs to provide to you if they have to verify your ID over the internet.
Have you called the Land Registry? They may be prepared to verify you over the internet. Or I believe they can give permission for another type of profession to verify.
If not maybe a conveyancer would be cheaper than a solicitor?
Or keep trying until you find one at the right price. They vary enormously.