In Act 5 of Hamlet, one of Hamlet's main problems is his inability to act in order to avenge his father. Why is he having so much trouble with this?

I don't think your question is necessarily entirely
accurate. Whilst in the play Hamlet's procrastination is definitely a theme that we can
identify, at the same time, mostly this procrastination has come to an end, and in Act V
scene 2, when he is speaking with Horatio, Hamlet clearly displays his readiness to do
what it takes to avenge his father and also he shares his belief that his life will be
resolved. The many preoccupations and worries that had clouded his mind before,
preventing him from acting, are now over, and he is able to look forward and greet his
premature death and avenge his father.

From the beginning
there seem to be two concerns in the play. Hamlet is worried first of all whether the
Ghost is actually the spirit of his father or an evil spirit trying to tempt him to
commit a crime that will condemn him to hell. This is of course why he devises The
Mousetrap to try and catch "the conscience of the King." Secondly, there is a conflict
between the Christian faith and its ideas of forgiveness and then an earlier, more pagan
faith with its ideas of bloody justice and vengeance. Hamlet is worried that, by
listening to the Ghost, he is ascribing to this earlier faith and may be eternally
punished because of his vengeance.

However, if we look at
Act V scene 2, we can see that Hamlet is finally at peace within himself and his
immediate future. Note what he says to Horatio when asked about his business in
Elsinore:

It
will be short,

The interim's mine, and a man's life's no
more

Than to say
one...

We can see hear Hamlet
is at peace with himself and the future that he knows he must take in avenging his
father and greeting the fate that awaits him. He is procrastinating no longer and knows
that some kind of showdown is imminent.