What are two quotes in Acts 4 and 5 of Macbeth that show how Macbeth has become insane, with an explanation of the quotes?

Macbeth's mind has become more unstable since killing Duncan and Banquo.

The fact that Macbeth is conjuring witches and asking them for advice shows a little bit on instability.  However, accepting that he is otherwise sane and there is just magic afoot, Macbeth is well into a downward spiral by the fourth act.  He is getting more and more paranoid, and his paranoia continues his murder spree.

Killing Banquo because he might have been suspicious...

Macbeth's mind has become more unstable since killing Duncan and Banquo.

The fact that Macbeth is conjuring witches and asking them for advice shows a little bit on instability.  However, accepting that he is otherwise sane and there is just magic afoot, Macbeth is well into a downward spiral by the fourth act.  He is getting more and more paranoid, and his paranoia continues his murder spree.

Killing Banquo because he might have been suspicious (and because the witches said his sons, and not Macbeth’s, would be king) was just the first of Macbeth’s murders.  He seems to think that time itself is against him.

Time, thou anticipatest my dread exploits:
The flighty purpose never is o'ertook
Unless the deed go with it; from this moment
The very firstlings of my heart shall be
The firstlings of my hand. (Act 4, Scene 1)

These are the ravings of a madman.  Macbeth is basically saying that if he thinks it, he will do it.  He decides that Macduff is a threat, so he will kill Macduff.  He sends murderers to kill Macduff, and they kill his wife and son.  Lady Macbeth is worried that her husband has lost his mind.  Even though she does not know the details, she is afraid.  She confides in Ross, who tells her to have patience.  She responds that Macbeth is the one with no patience.

He had none:
His flight was madness: when our actions do not,
Our fears do make us traitors. (Act 4, Scene 2)

The fact that his wife, who planned the murder of King Duncan so meticulously, thinks that Macbeth is mad shows how far he has gone.  By the time Malcolm and his army are storming the castle, Macbeth’s wife is dead and he has lost his faith in himself.

Out, out, brief candle!
Life's but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury,
Signifying nothing. (Act 5, Scene 5)

Proof of the fact that Macbeth has lost his mind is his reaction to Macduff when the two meet in battle.  He was told two seemingly contradictory prophecies by the witches, that no man born of woman can hurt him, and that he should beware Macduff.  When Macduff tells him that he was “from his mother's womb/Untimely ripp'd” Macbeth loses all confidence that he is safe (Act 5, Scene 8).  It is actually pretty easy for Macduff to kill him then.

Macbeth was not all too sane to begin with.  It was very easy for him to be manipulated by the witches and his wife.  Soon he was killing left and right to protect a throne he wasn’t even sure he wanted.  Macbeth’s downfall seemed inevitable. He was destroyed by his own ambition.