Is the buyer entitled to return the car and recover its full price after five months of purchase, knowing that there was a pre-existing defect in the gearbox and the buyer was informed of it before the purchase?

As long as you clarified to the buyer, concealed nothing from him, and no fraud or deception occurred on your part, and then you gave him a month's option; he is not entitled to return the car and take back the price due to the malfunction that occurred after five months.