It doesn't look good.
From landing to take-off, you need to:
Leave the airport (get off the plane, immigration, pick up luggage) - will probably take between 30 minutes and an hour, but may be significantly more.
Wait for a taxi. With some luck it's no time, but you never know.
Drive to Newark - according to Google Maps driving time is 1:20 hours.
Arrive at the airport 1:30 hours before take-off.
This adds up to at least 3:20 hours, while you have 4:05. So you might make it. But a delay in any of these stages will easily make you miss your flight.
What can go wrong? Your flight to JFK may delay, long lines at immigration or security, bad traffic and more.
Your willingness to risk it highly depends on whether your flights are booked as one or two tickets. If it's one ticket, and you miss your connection, the airline will take care of you. If it's two tickets, then it's your responsibility to show up on time, and you'll need to buy a new ticket from Newark to Ithaca.