Is it permissible to add 5 EGP to the price of a prescription in exchange for explaining the medication and its related warnings, without the patient's knowledge, and is this act unlawful (haram)? If so, how can one atone for it?

What the questioner referred to as the "price of service" is a fee for explaining the medication. The contract of ijarah (leasing/hiring) is based on honesty and clear disclosure. Therefore, it is not permissible to take this fee without the knowledge of the payer. The contract itself is not valid unless the contracting party is aware, and there is an offer (ijab) and acceptance (qabul). If explaining the medication is customarily expected from the pharmacist, then it is not permissible for the questioner to take this money, and he must return it to the patients, or seek their absolution, or give it in charity on their behalf if they cannot be reached. This is along with guaranteeing it to them if they can be reached later and do not approve of the charity.