In Act 5 scene 1, of Shakespeare's Hamlet, describe the relationship between Hamlet and Laertes. Give examples from the play for support.

In Shakespeare's Hamlet, you may
remember that at the start of the play (I.iii), when Laertes is departing for school,
Laertes (and Polonius) warns Ophelia about Hamlet and his attentions toward her. Laertes
tells her that he will use her, take her virginity, but never marry her because he must
serve the state and marry someone appropriate to his position of prince, but will forget
Ophelia. So we know at the start that Laertes does not have an overly favorable regard
of Hamlet—specifically in terms of Ophelia's relationship with
him.

In Act Five, scene one, Laertes has returned to news
of his father's death at Hamlet's hands. (As a note, now Hamlet, Laertes
and Fortinbras have lost their
father.)

This is the scene in the cemetery, where Hamlet
speaks the famous line about the court jester during his youth, whose skull he
holds:

Alas,
poor Yorick! I knew him,
Horatio... (lines
172-173)

As Horatio and
Hamlet speak, Hamlet realizes that there is a burial taking place nearby, looking as if
the death had been a suicide ("maimed rites"). Laertes is there, speaking, and Hamlet
makes note of it: speaking admiringly of him.

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That is Laertes, a very noble youth.  (line
217)

As they
listen, Laertes asks that more be added to the funeral service, perhaps a mass. The
priest refuses, stating that "she" is lucky to be buried in holy ground at all—and only
by the order of the King. Laertes goes into the grave to embrace his sister once more,
and then Hamlet, realizing the body is that of Ophelia, does the same, noting that he
also is devastated by her death.

Laertes springs to attack
Hamlet, cursing him:

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The devil take thy soul! (line
257)

Hamlet tries to remove
Laertes' hands from around his neck, warning Laertes of danger if he
continues:

I
prithee, take thy fingers from my throat;
For, though I am not splenitive and
rash, (260)
Yet have I in me something dangerous,
Which let thy
wisdom fear. Hold off thy
hand!

The two young men need
to be separated. Hamlet swears to continue to fight, and Gertrude asks Hamlet
why.

I loved
Ophelia. Forty thousand brothers (270)
Could not, with all their quantity of
love,
Make up my sum.

Hamlet then asks Laertes
what is wrong with him, to attack Hamlet. Hamlet admits that he has loved Laertes
always, bearing him no grudge:

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Hear you, sir!
What is the reason that
you use me thus?
I loved you ever.  (lines
291-293)

Hamlet is then led
away by Horatio.

In Act Four, scene seven, Claudius spoke
to Laertes about punishing Hamlet for Polonius' death. At the end of this scene,
Claudius reminds Laertes of that discussion. In this way, we know that Laertes is
committed to murdering Hamlet, with the King's
blessing.

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Strengthen your patience in our last night's
speech.
We'll put the matter to the present push.— (lines
297-298)

Hamlet did kill
Polonius, but it was accidental. He also has no way to know that Claudius is plotting
with Laertes, though he will understand it clearly enough when the "sword play" is
announced between the two men. Laertes' rage with Hamlet puzzles him here, but it will
make more sense when the competition between the two men is arranged, for Hamlet will
then suspect "knavery." Laertes has expressed his willingness to kill Hamlet—even in a
church (Act Four, scene seven), so it is safe to assume that where Hamlet is confused
about Laertes hatred for him, Laertes is committed to the purpose of ending Hamlet's
life.