FR 5569 then EI 109 at Dublin
Rome → Dublin → New York JFK
Timetable, Dublin time
23:55FR 5569 from Rome at the gate
13:40EI 109 to New York JFK leaves the gate
13 h 45 apart on the timetable, overnight
EI 109 leaves 13 h 45 after FR 5569 arrives on the timetable: more than half a day, so not a connection we count.