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.