Actually, it is against the law in NYC. The max number of people in a cab including the driver is five. Some drivers will take you anyway but when you get in the cab line at the airport they may not allow it.
I don't know what airport you are flying into but for five people it is easy and economical to hire a car service. Last month I flew into Newark and we took the Air Train to Penn Station. That worked well but I had my husband to carry the luggage. Ha! Ha! When I travel to NYC with my family I often use a car service. I've used Dial 7 recently. I have used others and the only one I won't use again so far is Carmel Car Service. Do not take Super Shuttle, you'll spend hours in the van.