I fly in and out of Orlando frequently, and it pretty much closes up at night. There will be no restaurants open in the airport at that time, and yes, TSA does not open until 5:00 AM. I was on a Delta flight last week (August 9, 2016) when Delta had their meltdown. My flight arrived at 2:00 in the morning, everything was locked up. You could probably sleep on a bench, but I did not see anyone hanging around any areas outside of the arrival gates. I would highly recommend getting a good night's sleep at one of the hotels nearby. Many of them have shuttle that pick up at the airport. There are no food courts that stay open past about 10:00 PM, and they don't open until about 6:00. Hard to find something to eat real early there.
Check on booking.com, or trivago and see what you can find for a hotel. I don't think Orlando has any flights that actually leave at 5:15. Most flights don't leave before 6:00 AM.
If nothing else, you can hang around a hotel lobby, but Orlando really pulls in the sidewalks after about 11:00 (or earlier) Even in the hotels, their lobby bars or restaurants are closed after 11:00. I think the airport lounges also close. (like Delta or American's sky clubs)
Good luck!