If the worshipper gets up for a fifth rak‘ah in a four-rak‘ah prayer, what should he do?

The imam, the one who is praying on his own and the one who is praying
behind an imam come under the same ruling with regard to doing extra rak‘ahs.
If any of them them adds a rak‘ah deliberately, knowing that it is
additional, his prayer is invalidated; but hardly anyone does that. 

But if the addition to the prayer was by mistake, then either the worshipper
(whether he is an imam, praying behind an imam or praying on his own)
realizes that it is something additional during the extra rak‘ah, in which
case he must sit back down immediately, otherwise his prayer will become
invalid, because he deliberately added something to the prayer. He must also
recite the tashahhud if he did not do so previously, and prostrate twice
(the two prostrations of forgetfulness) after the salaam. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: The phrase “if he
realises” means: if he realises that it is something additional during the
additional rak‘ah itself. 

The phrase: “he should sit back down immediately” means: as soon as he
realises it, and he should not delay; even if he remembers whilst bowing
that this is an additional rak‘ah, he should sit down. 

Some seekers of knowledge may think that the ruling on this issue is the
same as the ruling on one who stands up following the first tashahhud and
thinks that if he has stood up for the extra rak‘ah and started to recite,
it is haram for him to sit back down. This is a mistaken notion, because one
should never continue with the additional rak‘ah. As soon as he realises, he
must sit back down, in order to put a stop to this additional rak‘ah,
because if he continues with it when he is aware of it, he will be adding
something to the prayer deliberately, which is not permissible and renders
the prayer invalid. 

The phrase “must also recite the tashahhud if he did not do so previously”
means: when he realises that he is doing something additional and sits back
down, then he should recite the tashahhud, unless he recited it before he
stood up for this additional rak‘ah. But this begs the question: is it
possible that anyone could get up to do another rak‘ah after reciting the
(final) tashahhud? 

The answer is yes, it is possible, if he recited the tashahhud in the fourth
rak‘ah, then he got confused and thought that it was the second rak‘ah, so
he got up for what he thought was the third rak‘ah, then after standing up
he realized that this was a fifth rak‘ah and that the tashahhud he had
recited was the last tashahhud. The words “he should prostrate and say the
salaam” clearly mean that he should prostrate (the two prostrations of
forgetfulness) before the salaam. This is the adopted view, because they do
not think that the two prostrations of forgetfulness should be done after
the salaam, except in the case where one has said the salaam before
completing the prayer. But in all other cases, it should be done before the
salaam. However the more correct view, which was favoured by Shaykh al-Islam
Ibn Taymiyah, is that two the prostrations of forgetfulness for adding
something to the prayer should be done after the salaam in all cases. 

Question: if a person gets up for a third rak‘ah in Fajr prayer, what should
he do? 

Answer: he should sit back down even if that is after bowing; he should sit
back down, recite the tashahhud and say the salaam, then do the two
prostrations of forgetfulness and say the salaam again, according to the
more correct view, which is that in this case the prostration should come
after the salaam. 

End quote from ash-Sharh al-Mumti‘, 3/342-343

 But if the worshipper did not realise that he had done something extra
until after he had finished the prayer, then in this case his prayer is
valid and the two prostrations of forgetfulness should come after the
salaam, for the extra actions that occurred during the prayer. 

In Majmoo‘ Fataawa Ibn ‘Uthaymeen (14/31) there is a question about a
man who prayed Zuhr with five rak‘ahs, and did not realise until he was
reciting the tashahhud. What is the ruling in this case? 

He replied: If a person does an extra rak‘ah in his prayer, and does not
realize until he has finished the rak‘ah, then he must do the two
prostrations of forgetfulness; these two prostrations should come after
saying the salaam at the end of the prayer. The evidence for that is the
fact that when the Messenger (blessings and peace of Allah be upon him)
offered a prayer with five rak‘ahs, and they told him about that after the
salaam, he prostrated twice. As he prostrated after the salaam, and did not
say that the two prostrations for having added this rak‘ah should come
before the salaam, we know that the two prostrations for having added
something to the prayer should come after the salaam. This is also supported
by the hadeeth of Dhu’l-Yadayn. End quote. 

And Allah knows best.