The Great Gatsby was published in 1925. In those days there was fairly strict government censorship as well as self-censorship among respectable publishers with regard to descriptions of intimacy between men and women. The federal government could ban boks from being sent by U.S. Mail; local governments could ban the sale of books in book stores. The Roaring Twenties supposedly broke down female inhibitions to a considerable extent, but whatever they did occurred "offstage," so to speak. There is nothing in The Great Gatsby about the intimate relations between Tom Buchanan and Myrtle Wilson or those between Gatsby and Daisy, although the reader should have no doubt that both couples were having sexual relations.
At the end of Chapter V, Nick Carraway definitely feels that he is not wanted. "Two's company, three's a crowd." Fitzgerald had the good sense to begin the liaison between Gatsby and Daisy in Gatsby's house rather than in Nick's cottage. Otherwise, Nick would have looked like a panderer. The last paragraph of Chapter V reads as follows:
They had forgotten me, but Daisy glanced up and held out her hand. Gatsby didn't know me now at all. I looked once more at them and they looked back at me, remotely, possessed by intense life. Then I went out of the room and down the marble steps into the rain, leaving them there together.
This ending of the chapter is equivalent to a "slow fadeout" in motion picture parlance. It is going to be left up to the viewer's imagination what will be happening. Daisy will undoubtedly be staying there for a long while. Gatsby has obviously gotten over his initial shyness, and they have both gotten over the awkwardness they felt when they met again for the first time after so many years. Nick would be very dense, very gauche, if he continued to hang around when they obviously want to be alone together. Daisy at least expects Nick to understand what she wants.
Fitzgerald has her hold out her hand to Nick. This is very significant--and would have been even more significant to a reader in 1925. This is to signify that she is perfectly content to be there alone with Gatsby, that Nick does not have to feel responsible for her, that he can feel perfectly free and confident about her safety if he goes away. She might also be giving him her hand to thank him for bringing her and her lover together again. It doesn't matter at all about what Gatsby is thinking, but it is important for the reader to feel that Nick is behaving like a gentleman, and for Nick to feel that he is behaving like a gentleman, when he leaves Daisy there to renew her intimacy with her lost lover.
An excellent comparable example of the "slow fadeout" employed by authors of novels in the 1920s and 1930s is to be found in Dashiell Hammett's The Maltese Falcon, which was published in 1929. This is a hardboiled novel full of violence and murders, but intimate relations between men and women, including those between Sam Spade and Iva Archer and between Sam Spade and Brigid O'Shaughnessy had to occur "offstage." The following is the ending of Chapter 9:
She put her hands up to Spade's cheeks, put her open mouth hard against his mouth, her body flat against his body.
Spade's arms went aorund her, holding her to him, muscles bulging his blue sleeves, a hand cradling her head, its fingers half lost among red hair, a hand moving groping fingers over her slim back. His eyes burned yellowly.
And then: Slow fadeout.