What does Macbeth's reaction to Lady Macbeth's death reveal about their relationship and his state of mind in Act 5?

Macbeth is despondent when he learns of her death, and his sorrow contains some of the most quoted lines in all of Western literature:

She should have died hereafter;
There would have been a time for such a word.
Tomorrow, and tomorrow, and tomorrow,
Creeps in this petty pace from day to day,
To the last syllable of recorded time;
And all our yesterdays have lighted fools
The way to dusty death. 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."  (5.5.17-27)

After news of the queen's death, Macbeth himself resolves to die, rushing into battle, crying out, "Blow, wind! come, wrack! 
/ At least we'll die with harness on our back! (5.5.50-51).   

In Act 5.8, Malcolm reports that Lady Macbeth died "by self and violent hands," and that all attempts to prevent the witches' propheices from coming to pass have failed.  The tragedy of Macbeth is complete.

By the way, you can view the full text of Hamlet, side-by-side with its modern translation by following the second link below.