5 weeks is too short to expect to get anything. To get money out of the bank, the bank wants to see a grant of probate, and to get a grant of probate, the solicitor needs to value everything she left behind (so they can fill in the inheritance tax return), get the executor(s) to swear the probate oath and submit it all to the court. If it turns out that there are more debts than money available to pay anyone named in the will, then you won't get anything. The solicitor might tell you that you are named, but whether you will get anything at all is something nobody can know until the solicitors have done all that work, paid any debts and paid the inheritance tax (if any).
I know - I did all this without a solicitor for my Dad when he died and it took a couple of months just to get all the paperwork done and get the grant of probate.
Do the solicitors even know your address? You won't have heard anything if they don't know how to contact you!
You say there's a will. In that case, heir hunters are TOTALLY irrelevant. What they exist for is if there's no will and nobody knows of any relatives who would be entitled to receive something. Most of what they do is family history research to find out if there ARE any relatives nobody knew about, and if there are, help those relatives claim what they're entitled to and take a percentage to pay themselves for their work.
Why don't you contact the solicitor? That will answer all your questions.