Two days covers the Colosseum and the Vatican if you start at opening and do not stack them. Three days is the comfortable minimum for Trevi at dawn and Trastevere without treating the metro as the holiday.
2 days: ancient Rome and the Vatican
Day one: Colosseum, Forum and Palatine at 8am, Pantheon after, dinner in Trastevere. Day two: Vatican Museums at opening, St Peter’s, then Campo de’ Fiori. Skip Borghese. Trevi only if you can do 6:30am on one of the mornings.
3 days: city plus neighbourhood
Keep the two-day core, then give day three to Trevi at dawn, Piazza Navona, and a slower lunch after 1pm. This is the version that still feels like Rome rather than a queue. Borghese if you pre-booked and still have legs.
5 days: Rome and Tivoli
Three city days, one Tivoli weekday (Hadrian’s Villa, Villa d’Este), and one buffer for heat or a second trattoria night. Stay in Trastevere or Campo de’ Fiori so you are not commuting across the city each morning. Then Frecciarossa to Florence — about 1.5 hours if you booked Trenitalia or Italo ahead.
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