Most cities have a Roman ruin. Split lives inside one. Around 300 AD Emperor Diocletian built himself a retirement palace on this peninsula, and when the nearby city of Salona fell to Avars and Slavs in the 7th century, refugees moved into its walls and never really left. Today about half of the old town is the palace: people hang washing in the lanes, a cathedral sits in the emperor's mausoleum, and the main square is a Roman courtyard with a cafe terrace on it. The historic center has been a UNESCO World Heritage site since 1979.
That alone would be a good weekend. Five days works because Split is also a proper working city with its own rhythm. There is a green market and a fish market where people actually shop, a forested hill (Marjan) with pebble beaches at its foot, a city beach (Bačvice) where locals have played a ball game called picigin in the shallows since 1908, and a harbor that is the gateway to half the Adriatic. From here Trogir, Krka National Park and the Cetina canyon are all a day trip away.
This guide is written for the off-season, roughly November to March, when the cruise crowds are gone and the city belongs to its residents again. Days one to three stay in the city: the palace, then the Riva, markets and Varoš, then Marjan and Bačvice. Day four is Salona and Trogir, day five Krka. The island trips that fill summer itineraries are in the "more time" section with an honest note on what actually sails in winter. Start on a Tuesday: the Museum of the City of Split and the Meštrović Gallery are closed on Mondays, and this order keeps the fish market away from Sunday. More on Croatia as a whole is on the Croatia country page. If you are continuing south, 5 Days in Dubrovnik picks up where this one ends.