NYC confuses me. First you've got the boroughs, then you've got other names like Farmingham or Sheepshead. Is Brooklyn a city or really kind of like a county, then these other places are cities inside a huge city?
The five boroughs of New York City represent 5 of the 62 counties of New York State. (Brooklyn is actually Kings County, and was an independent city until 1898). Within each county/borough, you also have distinct neighborhoods. There's more info
here and
here...