@Alfred, but usually bookshelves are 6-10 shelves high. So that would be 9 miles of books which is fairly doable if you consider that not only do they stack on top but they also have several rows, so 20-30 rows of books cuts this down to .3 miles.
The place I work has 3M items in their biggest library alone and they have 5 libraries + access to online papers, books, datasets etc. 5M items is indeed par for the course in a large library which you would find at least a couple of those in NYC, University libraries easily have several million items and you can usually use inter-library loan programs to get any book you want from anywhere in the world. Library of Congress has 32M items.
NYU has approximately 5M items in their library (4.5M according to their website) so they may be referring to that.
Items (which is what Libraries use to quanitfy their Library) do not necessarily mean books. They are documents, letters, pictures etc.