DL 5035 then DL 6063 at JFK
Chicago O'Hare → New York → Lima
Timetable, New York time
16:57DL 5035 from Chicago O'Hare at the gate
12:50DL 6063 to Lima leaves the gate
19 h 53 apart on the timetable, overnight
DL 6063 leaves 19 h 53 after DL 5035 arrives on the timetable: more than half a day, so not a connection we count.