Perche

I don't think you have time to see as many worthwhile things as possible. You only have enough time than to see one major thing, and to eat. If you have no luggage, figure about an hour and a half to get from FCO to the downtown train station (Termini) via Leonardo Express.

The Coliseum and the Forum are close together, and fairly close to the Termini. If you are a good walker you can walk from Termini and see the Coliseum/Forum in about two very rushed hours, or three hours slightly more casually. That's already 3.5-4 hours.

As far as food, unfortunately the Coliseum puts you in a prime tourist area. People sometimes think that you can just drop into any place in Italy and eat a delicious meal. That is absolutely false. Restaurants in italian tourist areas couldn't care less about their food. They know that tomorrow the customer will be in another city or continent. They cut lasagna or pizza off of a frozen block, microwave it and serve it to you (Tourists used to Olive Garden, etc, tend to drool over it anyway).

Also restaurants in Italy, outside of the touristy places, close at 3PM. In my opinion it may be worth investing in a cab in order to eat a decent meal, given your flight times, which give you a very narrow window for decent food.

Near Termini, since you are pescatarian (as am I), see if you can make it to Tempio di lside before they close at 3. It's only a few blocks away. Superb italian seafood, yet not a budget breaker. You will never forget it. http://www.isideristorante.it

Considering that you then have to get back to Termini, take the Leonardo Express back to FCO, clear security, etc, which is about 3 hours minimum, you don't have time to see, "as many worthwhile things as possible." You barely have time to see the Coliseum/Forum, eat, and get back to the airport.