Bridgie,
5 AM is too early to get up!!! But I've had to take friends to the airport, so I feel your pain. Even at 5 AM, it does depend on where you are starting from.
When we lived on the Cassia (NW Rome), we could jump on the GRA and be at the airport in about 20 minutes. But now we live down next to the Vatican, so we have to allow about 25 minutes! The Vatican is still on the WEST side of the river... so if you're really downtown (EAST of the RIVER), better allow 25-30 minutes...
If you're taking a taxi - Great; Call the service (or have your hotel do it) the day before. Taxis usually DRIVE FAST! It's kinda of the like the flight before the flight!!!! From Termini they usually go out C. Colombo which means traffic lights! But at 5 AM, they probably won't stop anyway!
If you're "driving," and if you're renting, better allot time for dropping off your car!
Good luck in your trip... 5 AM is not a bad time to drive/ride... if you get into rush hour here, often the train is a better alternative!
Ciao,
Ron