There would actually be some debate as to whether or not the play's climax lies in this final Act. Some would say the murder of Duncan is climactic, since it demonstrates the moment of immorality in Macbeth. He has been loyal and brave, and in that act alone he becomes treacherous and sinful through an act he cannot take back. So his morality is forever lost. Others would argue Act Three, etc... But for this question we will deal maybe with what the climax of Act Five is.
There are two arguments here, or two different types of climaxes here. Macbeth's "Tomorrow, and tomorrow, and tomorrow" speech has to be dealt with. Lady Macbeth has been pronounced dead by Seyton, a messenger; and in this moment, Macbeth explores the finality of life. It becomes a psychological climax as he expounds, "Life's but a walking shadow...a tale told / Told by an idiot, full of sound and fury / Signifying nothing" (V.5.17-28). All things come to an end, all of us go through the action of life with starts and stops, fits and passions, only to become dust, only to all end up in the same place.
Then there is the climax of action, the physical fighting between Macduff and Macbeth in Scene 8. Macduff is avenging the death of his family, Malcolm is storming the castle to take back his rightful throne, Macbeth is trying to hang on as his allies dwindle. All this starts with "turn hell hound, turn!" (3), Macduff's line in Scene 8. Finally the tyrant is killed and order in Scotland is restored.