What is the ruling on the prayer of one who was certain of the correctness of the prayer and did not alert the Imam, but rather performed a fifth rak'ah with him? And what is incumbent upon the one who thought the prayer was incomplete and caused an increase in the prayer?

If only one worshiper alerts the Imam, the Imam should not act on his word unless he is reasonably certain of its truthfulness. In such a case, he should act based on his strong presumption, not merely on the worshiper's glorification. The worshiper who alerted the Imam has fulfilled his duty, because doubt regarding a deficiency in prayer is treated the same as certainty of it, and "Whoever experiences something [unexpected] in his prayer should say: SubhanAllah (Glory be to Allah)."