Is the prayer valid if one joins the Imam while he is prostrating in the first rak'ah, and then the Imam mistakenly performs five rak'ahs while the follower completes four rak'ahs and makes the taslim with him, and then performs the prostrations of forgetfulness after the taslim?

If the Imam stands for an extra rak'ah, the congregants must alert him. He must then return [to the sitting position] unless he is certain of his own correctness; otherwise, he should not return nor perform the prostration of forgetfulness (sujud as-sahw). Congregants who are certain of the Imam's error should not follow him; rather, they should sit and perform the taslim with him. Whoever follows the Imam while aware of the addition and the impermissibility of following, their prayer is nullified. As for whoever follows him out of ignorance, forgetfulness, or doubt, their prayer is valid according to the most apparent opinion. A latecomer (masbuq) who becomes aware of the extra rak'ah and follows the Imam must repeat the prayer. If he was unaware, the most apparent opinion is that the extra rak'ah is not counted, and he must also repeat the prayer.