Could this be the first part of the five-part miniseries, The 10th Kingdom (2000)...?
The 10th Kingdom is an American fairytale fantasy miniseries written by Simon Moore and produced by Britain's Carnival Films, Germany's Babelsberg Film und Fernsehen, and the US's Hallmark Entertainment. It depicts the adventures of a young woman and her father after they are transported from New York City, through a magical mirror, into a parallel world of fairy tales.
The miniseries was initially broadcast over five nights in two-hour episodes on NBC, beginning February 27, 2000. It won an Emmy Award for Outstanding Main Title Design in 2000. The premiere had over 14.04 million viewers.
It's not a perfect match by any means, as a man -- the janitor of an apartment building -- is given a magic bean (rather than a hand) that grants him six wishes (rather than five).
However, the story is mostly set in New York, and the man does wish for a never-ending supply of beer, with the number of beers in his fridge doubling each time he closes and opens the door.
He later wishes for a million dollars, and a bag full of money stolen during a bank robbery appears outside his front door. The police show up a few minutes later and arrest him.
While he's being driven to the station, the man wishes he could escape from the police car, and subsequently ends up running from the police on foot through Central Park.
You can view the scene where he wishes for the beer at the 37:34 mark in the video below. He wishes for the money at the 44:37 mark. The police show up at the 48:10 mark. And he wishes to escape the police car shortly after the 52:17 mark.