Hi Vando.
All you can do is put in the numbers that you have from the nursing home and old bank statements.
The bank cannot give you more information for privacy reasons until you are made the Administrator of the estate at which time you become the legal personal representative of the estate. An estimate is usually very acceptable. If there are new assets that you find after the grant has been issued, then all you need to do is send the Court an affidavit with an updated inventory of property. Nothing to worry about, really.
Once you are the administrator you are legally responsible for administering the estate according to the state laws.

By the way, when you send the nursing home a copy of the Grant of Letters of Administration, they will issue a cheque or transfer the money to an account in the name of the deceased, typically “The estate of NAME.” They will not release the money directly to you. So do not close the bank accounts until all the transfers have been made.

Kind regards,
MV