Why does Hamlet appoint Fortinbras successor to his throne in Act 5?This question is from the play Hamlet, Act 5.

The answer to this question has its origins back in Act 4
when Hamlet sees Fortinbras and his army marching toward their battle in Poland.  Hamlet
asks several questions about this battle and learns that Fortinbras is heading into a
fight over a piece of worthless land, and Hamlet seems to question why so many men would
so willing go to their deaths for that, but realizes that there must be something rather
inspirational about Fortinbras that he can convince his army to do it.  In that scene he
calls Fortinbras a "delicate and tender prince" and while I don't know if that is really
true, (remember that he was originally planning an attack on Denmark with a bunch of
mercenaries!) Hamlet's perception is what matters and what influences his decision in
Act 5.  He respects that Fortinbras is taking strong action for something more about the
honor than actual physical or monetary gain.  Hamlet has been acutely aware of his
inability to act for the honor of his father and clearly sees what a foil Fortinbras is
to himself. 

In Act 5, after Claudius's death, Hamlet is
technically King for about 5 minutes and in those 5 minutes he does what he thinks is
best for Denmark.  He leaves Denmark in the strong and determined hands of a noble man
who is able to form a plan and carry it out; who seems fearless; who acts for honor's
sake; and who Hamlet thought was fine prince.  While it is not ideal to leave the
kingdom in the hands of a foreigner, what other viable options are left?  Horatio is not
noble and not Danish.  The kingdom of Denmark with the loss of its entire noble family
would be thrown in political and social chaos if strong leadership doesn't take the
reigns, and Hamlet ensures that that is what happens.