Jay Gatsby took Nick to New York for lunch because he wanted to tell Nick something. However that something was only telling nick that Jordan was going to tell him something for Gatsby. On the Car ride over Gatsby tries to clear his name of any rumors but only makes himself more suspicious. While in New York they're eating with a gangster who's one of Gatsby's "business partners". At the end of the chapter Tom shows up and nick tries introducing him to Gatsby but Gatsby doesn't want to see Tom and dips.
After lunch with Gatsby, Nick goes to have tea with Jordan who tells Nick about Gatsby and Daisy's relationship. And that Gatsby wants Nick to invite Daisy over for tea so he can meet her.
When Gatsby shows up at Nick's house, he is extremely nervous. He tries leaving twice, just before Daisy arrives and when he first sees her he stubbles knocking over a clock while trying to leave. Although their reunion is quite awkward Nick leaves them alone slipping outside and by the time he comes back, the two are radiant with joy.
After the tea Gatsby invites Daisy and Nick over to his mansion because he wants to show off to Daisy, showing her the life he can give her. At the end of the chapter Nick wonders if Daisy can live up to the expectations of Gatsby. Gatsby had been waiting for their reunion for 5 years and Gatsby had surely built up some unrealistic expectations.
The beginning of Chapter 6 tells us the mysterious Jay Gatsby's past, and it turns out he doesn't really have a past except the past of James Gatz, a very ordinary very boring young adult. Jay Gatsby is a persona made my James Gatz when he first met Dan Cody. Using James's new persona he befriends Cody who invites Jay to sail the world with him. 
After a not so good first conversation Gatsby mentions he met Daisy before, so Tom decides to accompany Daisy to Gatsby's party. Tom sours the mood of the party and Daisy doesn't have a particularly good time either.