Travel from JFK,Terminal 1 to 960 Fifth Avenue

Taxi is easiest. There is a flat rate but the wait can be long. Easiest is never cheapest. The flat rate excludes tolls, tax, and other fees that could apply so by the time you add in the tip, you are looking at approximately $70. For a solo traveler going to the East Side, I like the Airport Express bus to Grand Central. https://www.nycairporter.com/schedules/ For your specific trip though, you will need to grab a taxi or the subway after the shuttle. Maybe that could be your happy medium because you avoid the Air Train and finding the subway and changing trains.

Agreed with the first poster than easiest is not the cheapest. But to provide you information on the cheapest way (which I would do if I didn't have a lot of luggage with me):

1. Take a Jamaica-bound AirTrain from Terminal 1 to Jamaica station. This will cost you $5 (starting 1 Nov, it will be $7.75 but you say you are flying next week) which you pay by MetroCard while existing at Jamaica station.
2. Jamaica station is the same station as the one labeled "Sutphin Blvd-Archer Av-JFK Airport" on the subway map. The E train stops there. Take a Manhattan-bound E train from Sutphin Blvd-Archer Av-JFK Airport to Lexington Av-53 St. That is normally the 9th stop if everything is running normally. A subway ride costs $2.75 regardless of distance.
3. Transfer to a Bronx-bound (uptown) 6 train at that station. Take it 3 stops to 77 St. No charge for transfer.
4. Exit and walk three blocks west to your destination.

Total cost: $7.75 (if you already have a MetroCard); $8.75 (if you need to buy a MetroCard as there is a $1 fee for new cards)

If you end up having to go to the Met, follow #1 and #2; in step #3, take it 4 stops instead to 86 St and then walk to your destination.

Are you traveling on a weekend? There are often service changes on weekends.

Exactly as Andrew says . The main disadvantage with a taxi , is the potential for horrendous traffic coming into Manhattan from the airport in southern Queens .

you can use taxi or I would use UBER. you can also use the car services just dial 777-777-7777 and they will send you a car. I'm not cure it's the cheapest but definitely I would think the fastest. I've done it many many times.

Here's what I do-which is a compromise.
Take the AirTrain to Jamaica as the others suggested. you can get the LIRR commuter railroad there to Penn Station - more expensive but much faster, cleaner and easier. Jamaica is a main stop for trains going into NYC so there will be trains frequently. Get the ticket just after you enter the station in the machine. One way Penn Station. Look at the board for the next train to Penn Station. it will be a bout a 20 minute ride. At Penn station, just take a cab.

So what did you do?

Taking a taxi from JFK would not have been my recommendation.

Unless you have global entry, how quickly were you able to leave JFK after arriving, waiting on line at immigration, and then waiting for your bags?

The fastest way would’ve been for you to take the air train to Jamaica, the E train to Lexington Ave/53rd St, and then transfer to the 6 train uptown to 77th St. That would put you on 77th and Lexington. You would then walk a mere 3 blocks to 5th Avenue as 960 5th Ave is on that corner.

Penn Station is out of your way which is why I did not recommend you taking the Long Island Railroad. Worse, for you to take a taxi from Penn Station to 960 5th Av would’ve meant you sitting in bumper-to-bumper traffic as the meter kept rising.

Thanks everybody!
In the end,I took the yellow cab after all,as I was alone and had two suitcases.