45-min would be an illegal change in JFK even if you were on the same airline and same terminal.
Since you are talking about seperate tickets, unless the IAD connection is on a fully-refundable ticket, I would leave at least 1.5hrs with 2hr or 3hr a better idea since you are on seperate tickets.

You will need to clear immigration during the end of the prime European arrival window, wait for your bags (if you checked one), clear customs, change from Terminal 3 to 5, re-check/drop bag (if you have one), clear security and get to the gate. Never going to happen. Keeping in mind that you will need to be at the gate in the required amount of time for Jet Blue (I don't know what it is though).