Generally, you must have claimed the federal earned income credit in order to claim the New York State and New York City earned income credits. However, due to NYS decoupling from IRC code changes after March 1st 2020, you may be eligible for NYS and NYC credit, if applicable, based on your NY recomputed FAGI and recomputed earned income.
As far as line 5, Is the IRS figuring your federal earned income credit (EIC) for you? If yes, you should check the yes box. Otherwise, check no.