In the story he tells Horatio at the start of act V, scene 2 what qualities does Hamlet show that he has not displayed previously?

The main quality that we are allowed to notice about Hamlet that had not yet been displayed before is his clever and canny personality.

The author explicitly states how Hamlet tells Horatio that he plotted to overcome Claudius' scheme to have him murdered in England by replacing the letter that would have called for his execution.

He also tells Horatio that he has no sympathy for Rosencratz nor Guildenstern as he felt betrayed. The wording of this paragraph allows the reader to infer that he is quite a resentful being nonetheless the author quickly explains that he is as well merciful of those who he treated wrongly, as he certainly did with Laertes.