This is a special case. You can search for people in the 1905 NY State Census at ancestry.com. Until recently, But, you probably would not find anyone because ancestry had only a few NY State counties available online. During 2014 ancestry updated their 1905 NYS census and now have most of the counties available. Read their db description since they state that the records for some counties were lost.
For the 1905 NYS Census, you can also go to SteveMorse and search by name. It is a different index and search engine that might yield different results.