The Leonardo Express train runs between FCO and Rome every 1/2 hour and takes about(??) a half hour. Puts you in Termini.
Or you could get a cab at 40 Euros each way. Running time probably similar.
Of course the whole process of getting off the plane and through security and customs will burn a bit of time. Somebody else who has done it recently will probably give you a better idea of this.
I think I'd choose to have those 5 hours on Sardinia. IMHO.
Romelle
Come back and do Rome right for an anniversary.