Give an analysis of the purpose and language in Act 1 scene 5.

Act 1 Scene V is an absolutely crucial part of Hamlet. It establishes the overriding theme of the play, provides a catalyst for the protagonist's actions, and begins the process of Hamlet's development as a character. In this scene, the ghost of Hamlet's father appears to him on the battlements of Elsinore and tells him that he was murdered by his brother Claudius, who also seduced his wife Gertrude. Here, Shakespeare is establishing the play's dominant conflicts: the external conflicts between Hamlet, Claudius, and Gertrude; and the internal conflict that Hamlet has with himself—how to reconcile his nature as a thoughtful Christian prince with his desire for terrible revenge. And from now on, the entire play will hinge upon this central theme.
Hamlet is an intelligent young man, highly educated and prone to introspection. He also takes very seriously his duty as a Christian prince, which among other things, involves following Christ's injunction to turn the other cheek. The Ghost, however, forces Hamlet to turn his back on his Christian principles as embodied in the New Testament and instead embrace the Law of Talon—an eye for an eye, a tooth for a tooth—as found in the Old Testament. This irruption of a wholly unfamiliar world, a world of a dark and distant past, into Hamlet's life completely upends all that he'd previously held holy and just. Now he realizes the full measure of Claudius's evil, he must reject everything he's ever believed in to avenge his father's brutal murder.
It's notable that the disruption of Hamlet's life by a voice from the past was accompanied by an archaic form of language used by the Ghost to tell the tragic tale of his demise. He uses expressions such as "murder most foul," and "harrow up thy soul," which even at the time would've been considered somewhat old-fashioned. But such language is entirely appropriate to a voice from the spirit world, a voice that hearkens back to the Catholic belief in Purgatory, something that would've been rather exotic to Shakespeare's overwhelmingly Protestant audience.
Religious language and imagery are also used by the Ghost in recounting the sordid details of his murder. He was asleep in the garden when Claudius crept up on him and poured poison down his ear. The parallels with the Garden of Eden are not hard to detect. Hamlet's father was in Paradise before Claudius came along, like the snake who tempted Adam and Eve:

The serpent that did sting thy father’s life Now wears his crown.

By using the imagery of the Garden of Eden and the corruption of humankind by Satan disguised as a serpent, the Ghost is shaking Hamlet out of his complacent worldview, one characterised by a combination of New Testament Christianity and Renaissance humanism. That said, although Hamlet immediately vows to take revenge, he will do so in such a way that he will remain true to his ideals, or as true to them as he can be. That is why he's going to pretend to be mad, or to "put his antic disposition on;" it also explains why he restages The Murder of Gonzago to try and expose Claudius's villainy; and it's the main reason why Hamlet appears to vacillate so much in carrying out his act of vengeance. He will carry out revenge, alright, but in a method more becoming of his values.
There's a certain lurid quality to the Ghost's language, especially in relation to his murder. He refers to a "vile and loathsome crust" upon his body. He also pulls no punches in relation to his betrayal at the hands of Gertrude and Claudius. Theirs is a sordid, corrupt relationship in which the royal bed of Denmark is a "couch for luxury and damned incest." This is very far from the kind of sophisiticated, intelligent discourse that the student prince is used to and in which he usually engages. Yet the words of his father's ghost have their effect, and it's noticeable that, as the play progresses, Hamlet's own language will become progressively more vulgar and profane. One only has to think of his vicious tongue-lashing of Ophelia in Act III Scene I: "Get thee to a nunnery." And even more extreme is the intemperate langauge used by Hamlet towards Getrude in Act III Scene IV:

Nay, but to live In the rank sweat of an enseamèd bed, Stewed in corruption, honeying and making love Over the nasty sty—

There is a close parallel here between Hamlet's words and those of the Ghost in relation to Gertrude and Claudius's "incestuous" marriage. This is not the language of a son towards his mother, much less of a highly intelligent Christian prince; it is the language of hatred and resentment, a holdover from an atavistic pre-Christian world in which brutality and revenge were the norm. The Ghost, and the language that he uses, act as a reminder to Hamlet and to the audience, that for all our outward displays of civilized learning and religion, in the very depths of our souls, we are never too far away from a more primitive past.