If the cab was owned by the driver, and not leased from a cab company, there was an exception that went up to 8 years.

What shows up on Google Search: "While it approved a maximum five-year age limit for taxis, the commissioners said that they eventually intended to allow some cabbies who own their own cars to keep them as long as eight years. The retirement ages for taxis will be phased in beginning Nov. 1."

There was also extensions allowed for CNG powered cars, minivans, wheelchair accessible, hybrid or other clean-air cabs.

https://rules.cityofnewyork.us/tags/vehicle-retirement-dates