When Fortinbras arrives at the end of Act 5 was he attacking Denmark? What was his purpose in Act 5?I want to make a point in an essay that when...

In Hamlet Act V, I do think
Fortinbras means to take Denmark.  I have seen it staged as a real cannon with real
troops: an invasion.  Among these is Branagh's film version Hamlet,
in which the Norwegian soldiers crash through windows as they enter the castle and
Marcellus is stabbed by bayonet outside the castle
gate.

Earlier, Fortinbras had wanted to take Denmark, and
his uncle (influenced by Claudius) warned him against it.  So, Fortinbras went after
Poland instead, as a concession.  But, isn't Poland a red herring all along?  Yes, he
gets the lands back from Poland, but that does not end his quest for revenge.  He wants
his cake and to eat it too: the lands give him no personal satisfaction.  And, as you
know, revenge is all about emotional satisfaction.

Isn't
Fortinbras' real goal Denmark all along?  He clearly wants personal revenge, but now
that Claudius has done that for him by killing King Hamlet, he's out for political
revenge (against the entire country).

Fortinbras is a
combination of Laertes and Hamlet when it comes to revenge.  He had been hell-bent on
emotional revenge (like Laertes) against Denmark, but luckily he is forced to back away
from his hot-headed plan.  In Act V he proceeds like Hamlet toward revenge, much more
deliberately and indirectly.

His excuse for fighting in
Poland could be a red herring to pass through Denmark, his real goal.  The irony is, of
course, that he gets no personal satisfaction from revenge, like Hamlet.  Fortinbras
realizes that all are losers when it comes to revenge: it leads only to tragedy,
personally and politically.