The rule that decides it: two islands in a week is a holiday; four is a series of ferry terminals. At five days you are firmly in one-island territory, and trying for two spends most of a day on boats you did not need to take.
The shape
Days 1-2: Athens. The Acropolis at opening, then slow down. Athens rewards two days and starts repeating itself after three for most visitors.
Day 3: the crossing, in the morning. A morning boat means you arrive with an afternoon rather than an evening, which is the difference between four island days and three.
Days 3-5: one island. Whichever you picked, stay on it.
Our Athens itinerary covers the city half properly.
Which island
The one that suits five days is the one you can reach quickly and does not need a car to be worth it.
Naxos is our default for the calm middle of a route - shallow sand on a bus route, and an interior if you want a second kind of day. Two nights only works as a route stop, so at five days you are giving it the whole island half. Athens to Naxos covers the crossing.
Paros is the connector, the easiest island to reach in the Cyclades, and the most forgiving if the wind moves your plans. Athens to Paros.
Santorini works if the caldera is the reason you are coming at all - but it is the priciest island and the most day-tripped, and five days does not leave room to also do it justice and see anything else. Athens to Santorini covers the ferry-or-fly decision.
The version where you never change hotels
Worth considering seriously, because it is the least stressful five days available in Greece.
Stay in Athens and take the Saronics as day trips. They are the only Greek islands you can genuinely visit on a day trip, and if your Greece trip is short, or built around Athens, they solve a real problem: a proper Greek island day without spending two days getting to one.
Hydra is the striking one - a stone amphitheatre of a harbour town where no cars are allowed at all. Athens day trips covers the options and the Saronic route covers doing more than one.
What to book ahead
The crossing, in high season. Everything else on a five-day trip can stay loose, and should - the wind reorders island days more often than anything else, and a five-day plan with no slack in it is a five-day plan that breaks.
When five days does not work
If you want the Ionian. Corfu and Kefalonia are reached from the western mainland rather than Piraeus, which costs you a travel day at each end. Five days is not enough for that shape.
If you want two islands anyway. Do it with the shortest hop in the Cyclades rather than a long one - but know that you are buying a ferry day with an island day.
The itineraries have the seven-, ten- and fourteen-day versions, and the island-hopping guide covers sequencing.