AA 5586 then AA 6004 at Charlotte
Sarasota → Charlotte → Gulfport
Timetable, Charlotte time
16:57AA 5586 from Sarasota at the gate
15:58AA 6004 to Gulfport leaves the gate
23 h 01 apart on the timetable, overnight
AA 6004 leaves 23 h 01 after AA 5586 arrives on the timetable: more than half a day, so not a connection we count.