Do you have GPS? I live in Hamden, and use the Merritt/Hutch and straight over the Whitestone to the Van Wyck. The typical bottlenecks even off-rush hour occur at the approach to the Whitestone (if you happen to have EZ Pass, it make the toll experience a lot shorter during heavy periods), the merge onto the Van Wyck where there has been construction making the merge worse, and sometime the last mile or so to the airport exit. I'm not sure about parking for the International terminal because on a trip overseas I usually have a driving service. The outlying lots are mostly long term. There is also a lot near an aerial shuttle train stop which you can Google for directions. I think the flight time makes it hard to avoid all congestion, but on pre-and post rush hour experiences, traffic can be very light and the trip for me less than an hour 45.
I can't vouch for traffic flow, or current construction, but I know some limo drivers use the Throgs Neck bridge if the Whitestone and Van Wyck are messed up. Not sure which Long Island highway it dumps you on, but it isn't all that much longer to JFK. I think it takes you into the airport entry from a different side. If you don't have GPS, you can do a Mapquest or similar route for the Throgs Neck method. To get to the Throgs Neck, you can still take the Hutch but then get on 95 W toward NYC which is clearly marked after you pass the Mount Vernon exits. The Throgs Neck exit off 95 is well-marked.
If you aren't used to it, the Hutch splits around New Rochelle. Make sure you don't follow the signs to the George Washington Bridge, which might also say to I95. Follow the signs for the Hutch south and the Whitestone. That would also get you to where there is access to 95 off the Hutch is if you need to use the Throgs Neck. There are actually 2 different entrances to 95off that stretch of the Hutch a few miles apart,, and the second one gets you to the Throgs Neck with less of 95 to cover.
Look at a map on line or otherwise and it would make it all less confusing. If you want to the terminal by 5, I agree that to be safe, you'd want to get to the Hutch no later than say 3:00. If traffic is okay, you would get there well before 5, even as early as 4 or better, but better safe than sorry.