Gatsby's most central dream that we can grasp by chapter 5 is acquiring Daisy to be his girl. By the end of chapter 5, Gatsby is "glowing" according to Nick. Daisy was found crying on the couch when Nick returned from being outside, and these tears seem to be happy tears. Gatsby takes Daisy to his house (Nick goes too), and Gatsby uses the opportunity to showcase his wealth. He gives Daisy the chance to see all of the rooms, his shirts, and they listen to a boarder play music on the grand piano. Previous to this chapter in Gatsby's life, he had been poor and because of Daisy's family wealth, unable to secure a relationship with her. They were just in different social classes and it seemed that their relationship from a previous time was never going to work. Here, Gatsby believes he has finally arrived and attained his dream of having Daisy.
In F. Scott Fitzgerald's novel, The Great Gatsby, it would seem in Chapter 5 that Gatsby will finally realize his dream of getting Daisy back into his life. However, there are signs that show that this will never be the case.
Gatsby has the money that he lacked before, which was something Daisy needed in her life. Now he can take care of her in the style in which she is accustomed, and she can choose Gatsby rather than Tom. She is aware of his wealth as she moves about his home. And Gatsby looks at her: having Daisy has been the only focus he has had for years. All he has done and achieved has been for her. However, it is for an idealized Daisy, a woman who does not exist in the present. This will make it impossible for him to fulfill his dream: he is looking for someone who does not exist.
Time is also Gatsby's enemy. In order to recreate the relationship they had years ago, he would have to return to that time: it is also impossible. What existed in the past remains there. They are no longer the same people, and his memory of her is based a great deal on his idealization of her.
Gatsby believes, symbolically, that Daisy, the "idealized one," had a light that beckoned to him, that was always shining, reaching out to him. However, the "real" Daisy does not have that light because she is not the essence of Gatsby's dreams or fantasies.
The eNotes summary describes what Gatsby faces now that Daisy is finally with him:
The enchantment had become his total being, had consumed him—no human could have measured up. Daisy must have 'tumbled short of his dreams—not through her own fault, but because of the colossal vitality of his illusion.'
Gatsby is looking for someone who does not exist. Daisy cannot be who he wants her to be because the person he is looking for is an illusion: someone who exists in his mind only, based on his perceptions of the past.