Is it permissible to fast if intercourse occurred five minutes before the dawn call to prayer?

If intercourse occurs before the adhan and concludes before it, the fast is valid. However, if it occurs during the adhan and the man withdraws immediately, there is no need for a makeup fast nor expiation. But if he continues, then both a makeup fast and expiation are required.

If intercourse occurs after the adhan, thinking it is still late [before dawn], and then it becomes clear that it was after the Fajr adhan, the fast is invalid, and a makeup fast is obligatory in all cases. Expiation becomes obligatory if the person engaging in intercourse continues after knowing that the muezzin has called the Fajr adhan. If he ceases immediately upon realizing, then there is no expiation, but a makeup fast is still required. The woman is like the man in all these rulings, provided she is consenting.

Imam An-Nawawi said: "If dawn breaks while he is engaging in intercourse, and he becomes aware of its breaking, yet he continues to sustain the intercourse, then his fast is invalidated without dispute... and expiation becomes obligatory according to the madhhab." He also said: "If he eats, drinks, or engages in intercourse, thinking the sun has set or that dawn has not broken, and then the opposite becomes clear... a makeup fast is obligatory upon him... And this is the view of Abu Hanifa, Malik, Ahmad, Abu Thawr, and the majority of scholars."