In Chapter 5, why does Gatsby get so many calls? What does this say about him ?

Gatsby is a most improbable person. He is a romantic gangster. Fitzgerald was young when he wrote the novel. He obviously knew very little about big-time bootlegging and other such racketeering. I believe his publisher told him that there ought to be some indication of exactly how the protagonist was making all this money. Since Fitzgerald didn't really know, he invented some telephone calls to create the impression that Gatsby was so high on the ladder that he could control a criminal empire just by receiving information and issuing orders over the telephone. In one of his telephone conversations Gatsby makes an amusing comment: 

"Well, he's of no use to us if Detroit is his idea of a small town."

This suggests all sorts of things. Maybe Gatsby is involved in passing counterfeit money or laundering money. It also suggests that he has "connections" all over the United States. Evidently he doesn't have to worry about his phone being tapped. The technology for doing this may not have existed when the novel was written.

Fitzgerald also introduces Nick Carraway to Meyer Wolfsheim for the purpose of demonstrating that Gatsby's partner knows all about the ways to make large sums of money illegally, how to eliminate competitors, and is willing to share the spoils because Gatsby's polish and charm give them entree to upper-class people who can provide protection and also have big money to spend and to invest. Wolfsheim talks about the real lives of mobsters and sounds like an authentic one himself. He admires Gatsby for being able to pose as a real gentleman.

"He went to Oggsford College. You know Oggsford College?"

"I've heard of it."

"It's one of the most famous colleges in the world.

"Have you known Gatsby for a long time?" I inquired.

"Several years," he answered in a gratified way. "I made the pleasure of his acquaintance just after the war. But I knew I had discovered a man of fine breeding after I talked with him an hour. I said to myself, 'There's the kind of man you'd like to take home and introduce to your mother and sister.'"

(Is it possible that Wolfsheim has a sister he is hoping to marry to his handsome partner? Would this explain why Gatsby can make money so easily?)

Gatsby himself has little to do but ride around in his roadster, fly in his hydroplane, pursue Daisy, and give his wild parties every week. If there is any dirty work to be done--as there surely must be in the big-time bootlegging business with competitors like Al Capone--he can issue orders over the phone or have Meyer Wolfsheim take care of it. Gatsby is a sort of "front man" for the mob, and the fact that he has been to Oggsford College makes him an intellectual who can deal with the more esoteric problems that arise. 

A lot of people wonder about Gatsby, including, no doubt, many of the readers. He is a man of mystery--perhaps even to his creator F. Scott Fitzgerald. There are all sorts of rumors about Gatsby. He does manage to keep a low profile in his Long Island mansion. Gatsby had to get rich quick if he wanted to catch up with Daisy. The only way to do that was illegally. But Fitzgerald obviously knew little about such matters and could only hint at them. This is a weakness in The Great Gatsby which is almost totally covered up by Fitzgerald's brilliant writing.