A rendering shows how Tower Fifth would look soaring over Manhattan.CreditCreditTMRW, via Gensler

The developer Harry B. Macklowe and his team — Moed de Armas & Shannon Architects and Gensler — submitted a preliminary application to the Department of City Planning outlining his intention to build a new super tower, east of Fifth Avenue between 51st and 52nd streets, overlooking St. Patrick’s Cathedral.

If approved at 473 meters tall, the skyscraper would rank as the second-tallest building not only in New York, but in the Western Hemisphere...