It is not possible to identify the actual decision maker who will be responsible for making a decision on your friend's ESA entitlement, but he/she will be based at the JCP/BD office which deals with the claim.
You can still send a copy of the ESA50 (although this is not an absolute requirement) and any relevant letters to the JCP/BD office before 5 August, and indeed you can send any evidence up until the date of the actual decision on ESA entitlement. However, as you will be unaware of the date on which the decision will be made, it is preferable to send the additional information as soon as is practicable, but the 5 August date should (this being the operative word) not present any problems.
Nothing on this board constitutes legal advice - always consult a professional about specific problems