I've got five hours in NY, what places can I visit in that time?

You likely don't have enough time to make it to Manhattan and back in time unless you want to really stress. If your 99-year-old grandma lived in Manhattan, I'd say get in a cab, get there, and bite your nails in traffic on the way back. It's probably worth it. But since your question implies there's nothing particular you'd like to experience, it probably makes sense to stay in the airport or make a quick trip nearby.

A few nearby options:

Coney Island is a relatively short taxi ride away (and a much longer train ride). Weekends can be fun there (Saturdays in particular), even during the winter. I once became friends with a two-headed cow there.

And it's true that Rockaway is close (also a cab ride). It's a beautiful beach, though it will be pretty empty during the cold months.

Jamaica Bay Wildlife Refuge is another notable location close to JFK. It's a spectacular birding destination during the Spring & Autumn, and although I've never been there during the winter, it's open then, and there seems to be plenty to do, especially on Saturdays.

Of course there's also Brighton Beach. Do you like vodka? How about dense bread?

Don't listen to the haters. You can make it out of the airport if you rush. But move fast and be prepared to spend money on taxis.

Realistically, probably nothing beyond the airport - at least not unless you want to pay for taxis.

The most obvious place to visit in New York is Manhattan, whether that be Times Square, Central Park, The Empire State Building, or pretty much any of the other major travel destinations.

Public transport from JFK to Manhattan is relatively easy, but it's not overly fast. Via either the Subway ($7.50 each way) or the Long Island Railway (LIRR, $12 each way) you're looking at around an hour (or more) each way from JFK to Manhattan or back. (LIRR will be slightly less, but only stops at Penn Station so you need to include the time to get to your actual destination).

You're going to want to be back at JFK at least an hour before your flight departs, which means you've only got 4 hour maximum. Allowing 2 hours for transit and an extra 30+ minutes buffer time, you're going to only slightly over an hour at your destination.

So if you do want to see a single place - preferably something that doesn't involve waiting/lining up to get into - then it's possible, but you're not going to get long there. You could certainly have a wander around the Times Square area, or maybe around a small corner of Central Park, but not much else.

The other alternative is to take a taxi which will probably be faster (traffic dependent), but much more expensive. Taxis trips between JFK and Manhattan have a fixed fare of $52, plus tolls (if any) and tips. This might knock 30 mins off of your travel time, so it'll give you a little more time - but not much more.

Will that give me enough time to visit one/any places in New York City

The simple answer is no, not even close.

If you have more time, there are many dupe questions such as https://travel.stackexchange.com/a/61646/19233