I am flying to JFK from Grenada by Jet Blue, arriving in Terminal 5 at 7.00 PM. My next flight with different ticket is in Lufthansa flying from Terminal 1 at 10.20 PM to Doha. I need to do immigiration, bags collection and security check and do the same in Terminal 1 for Lufthansa flight. Do i have enough time to do this within 3 hrs 20 min. Please advise.