The Church of Jesus Christ of Latter-Day Saints (LDS) have added the 1905 New York State census to their on-line collection. For now the census pages are only for browsing and have NOT been indexed. I noticed that most of New York City is not included, with the exception of Kings County (often referred to as Brooklyn). I suspect that the NYC census has not survived but most of the rest of the state is available.
The 1905 census did ask if a person was a citizen and how long they have lived in the US but they stopped asking for a state or county and just had “US” if born in this country.
To find the 1905 census records, go to FamilySearch (pilot) and then scroll down until you see a world map. Click on “Canada, USA and Mexico” and you get a selection page. Click on “New York State Census, 1905? and you will see a list of counties and then Towns to browse. Don’t skip this census even if you have the federal census for 1900 and 1910. You should find your families on every available census record. You may be surprised what you find.