There are a couple of statements by Macbeth in the final act that show he has accepted his fate. One occurs at the end of Act 5, Scene 5, when the Messenger tells him:
As I did stand my watch upon the hill,
I looked toward Birnam, and anon methought
The wood began to move.
Macbeth reacts with something close to terror. He says:
I pull in resolution, and begin
To doubt th' equivocation of the fiend
That lies like truth.
Then when he is confronted by Macduff on the battlefield, he learns that the other assurance he had been depending on was another equivocation. He believes that no man of woman born could overcome him. But Macduff unnerves him by telling him that he was not literally born of a woman because he had to be delivered by a caesarean section. This news coupled with the fact that Birnam Wood moved to Dunsinane seems to prove that Macbeth is doomed. He tells Macduff:
Accursed be that tongue that tells me so,
For it hath cowed my better part of man;
And be these juggling fiends no more believed,
That palter with us in a double sense,
That keep the word of promise to our ear
And break it to our hope.
Macbeth probably could have beaten Macduff in a sword fight under normal conditions. But he has lost his courage, his motivation, and his hope. He appears to be all alone against an army of ten thousand men. In spite of this, he has no choice but to accept Macduff's challenge to fight. Macduff has the advantage of being strongly motivated by his desire to avenge the slaughter of his wife and children, and he overcomes Macbeth without much trouble. He reenters near the very end of the play and presents Macbeth's severed head to the new king Malcolm.