I am looking for an apartment building with at least 50% occupancy, in
the tri-state New York area. The repairs, liens and the building
purchase total must not exceed $5,000,000. The profit (from the rent
roll minus expenses) if fully occupied, should be able to pay for the
building within 7 years or less.

In other words, you want the Net Operating Income of the building to
be more than 1/7 of the sales price.

In other words, you want a capitalization rate of 14% or better.

This is next to impossible to achieve today. Most buildings today are
selling for an 8%-9% cap rate or lower.

I want one too.  Why would you want to pay the building off anyways?