What are the five soliloquies that Hamlet has to speak?

As you say, there are five soliloquies that Hamlet speaks in this play.  They are:

• The one that starts "Oh that this too solid flesh would melt."  This one is in Act I, Scene 2.  He is very unhappy because of his father's death and his mother's remarriage.


• The next one is in Act II, Scene 2.  That one starts "Oh what a rogue and peasant slave I am."  In this one, he decides to trap Claudius by putting on a play.


• The third is in Act III, Scene 1.  This is the famous "to be or not to be" soliloquy.


• The fourth is two scenes later.  It starts "Now might I do it pat."  Here he doesn't kill Claudius and talks about how he didn't to do it when Claudius's soul might be clean.


• Finally, there is one in Act IV, Scene 4.  It starts "How all occasions to inform against me."  Here, he laments his inability to just go and kill Claudius.