How does Shakespeare present the idea of mortality in Act 5, scene 1 and how does this relate to Hamlet's character in the rest of the play?

Throughout the play, Hamlet has been meditating on death or mortality. Was his father's death murder or did he die a natural death? How should revenge take place? So far, most of Hamlet's thinking has been from the point of view of the afterlife. In his "to be or not to be" soliloquy, for example, his thoughts about suicide hinge on whether it will lead to oblivion--in other words whether he will melt away or evaporate like dew, which is what he would like--or if their actually is an  afterlife that might lead to hell. That fear of an afterlife keeps people from suicide, Hamlet thinks.

The afterlife is uppermost in his thoughts about killing Claudius as well: for example, he refrains from killing him while he is in prayer, because he doesn't want Claudius to go straight to heaven. 

In Act V, scene 1, Hamlet meditates on death from the point of view of how the dead are remembered by the living rather than from the perspective of the afterlife. He and Horatio stumble across a gravedigger digging a fresh grave, and Hamlet wonders, as he picks up a discarded skull, who it belonged to. The gravedigger tells him it's the skull of Yorick, the court jester. Hamlet remembers Yorick carrying him about on his back when he was a child and is shocked at the idea that Yorick now is reduced to this smelly skull. Hamlet thinks about death as the great leveller or equalizer of people ( a common trope of the Middle Ages and Renaissance)--and Hamlet muses that even someone like Alexander the Great is no more than dirt and dust now. 

Hamlet realizes in this scene that from the point of view of the living, we are all destined for the same fate, whether beggars or kings: to become a pile of bones that decay into dirt after a few short years. When he discovers the grave being dug is for Ophelia, and when the mourners arrive for her burial, he mocks their words and gestures of grief with his own hyperbole: they are not really going to do anything for her, no matter what their words: in reality her death means very little. 

All of these thoughts are in the mind of this most contemplative of men as he heads to the final confrontation with Claudius and Laertes. When he warns Laertes that there is something dangerous about him: "I have something in me dangerous,/Which let thy wisdom fear," he may be alluding to his lack of fear of death, for he knows we all end up as dust.