Was I required to pay 500 EGP for the hair straightening product that the salon worker opened before the appointment and without my permission, and what should I do if five years have passed since the incident and I cannot reach the worker?

This image might indicate either a promise to purchase or an authorization for the worker to make a purchase.

You are not obligated to take the item after its packaging has been opened in either case, as the agreement was to purchase a new, complete package.

In the case of a promise: The promisor is not obligated to fulfill their promise according to the majority of scholars. If any harm is incurred, it is due to the worker's action, not yours.

In the case of authorization: You are not obligated to accept anything that deviates from the agreed-upon description, and the worker violated this by opening the package.

Ibn Qudamah said: "The agent does not possess the right to dispose of anything except what is necessitated by the permission of their principal."

Al-Dardir said: "If the agent violates the terms of purchase, what they purchased becomes their responsibility."

In summary, you are not obligated to anything towards this worker, and if any harm befalls her, it is due to her own action.