Having lived in NYC for 15 years I would NEVER recommend a tourist or first time visitor to Manhattan use the subway system from JFK. That's fine for city dwellers, not fine for first time visitors with luggage and children.
Use Super Shuttle. Actually, with the group of 5, you can reserve your own shuttle without anyone else on it except your family, and it will be more economical as well, since they charge per person (about 18 dollars or so last time I used it).
I use Super Shuttle everywhere is is available from the airports to the hotel. I have never had a problem with them. They have a website and you just go on, reserve, pay and go. When you arrive at the airport, you check in at the trainsportation desk after customs, and they will dispatch the next available van to you while you wait. It takes 10 -20 minutes from checkin to departure.
You also have the option of taking the Airporter bus service, which stops outside all of the terminals at JFK and goes to Grand Central and the Port Authority Bus Terminal-- but you also pay PER PERSON for the bus, and then have to make your way from those stations to your hotel -- that still makes the Super Shuttle your cheapest option.
Forget the subway. It involves a connection from the airport to the train, then the trip into town with more and more people cramming on at each stop into NYC, and then another transfer or bus or taxi to your ultimate location once you arrive in NYC. Again, great for NYC residents that know exactly where they are going. Not good for visitors.