The climax of Shakespeare's Macbeth is probably not in Act V. Act III is usually thought to contain the climax.
First, climax is more when the conflict is decided, rather than when it is finally resolved. The conflict of Macbeth is not finally resolved until Macduff enters the stage holding Macbeth's head. The two leave the stage earlier and the outcome of their sword fight is in doubt. Macduff's entrance reveals that Macduff won the fight and Macbeth is dead. That's the resolution, however, not the climax.
Macbeth's fate is sealed and determined, though, in one of two scenes in Act III, depending on one's opinion. Unusually, the climax of the play may occur with a stage direction in Act 3.3: "[Exit Fleance.]". When Fleance escapes, Macbeth's attempt to defeat fate (in the form of the witches, who predict that Banquo's heirs will be kings) fails. He can no longer create a dynasty with his heirs. Some see this as the climax.
If one doesn't see this as the climax, another possiblity occurs in the very next scene when Macbeth sees Banquo's ghost and reacts in an insane manner. This is the breaking point of the play. The thanes present at the feast, if they don't know Macbeth is unfit to rule before this scene, certainly know it by the end of the scene. Furthermore, Lady Macbeth realizes during the scene that "the jig is up," so to speak. After Macbeth's "fit," maintaining power is impossible. Macbeth isn't overthrown until the end of Act V, but from this point on it's only a matter of time.