Sousse is two places that share one beach. The first is a walled medina, built up by the Aghlabid emirs in the 9th century as their main port, the harbor their fleets sailed from when they invaded Sicily in 827. It stands near the ruins of Hadrumetum, a Phoenician trading post that became the second city of Roman Africa after Carthage. The second is the hotel strip that runs north along the sea to Port El Kantaoui, built for package holidays, with a marina that opened in 1979 as a made-to-order tourist village. The medina has been a UNESCO World Heritage Site since 1988.
Honestly, the medina is small and you can see its three big monuments in a morning. What makes Sousse worth five days is where it sits. Kairouan, one of the holiest cities in Islam, is under an hour away. The El Jem amphitheatre is about an hour south. Monastir, with the oldest ribat in the Maghreb and the mausoleum of the man who founded modern Tunisia, is a short metro ride down the coast. You stay in one place, you unpack once, and you get Roman, Aghlabid and 20th-century Tunisia in separate bites. The beach day fills the gap, and it depends on the season: this is a summer resort, whose season traditionally runs from June to early October, and the sea is cool from January to April.
The plan: day one is the medina, day two Kairouan, day three the beach and Port El Kantaoui, day four El Jem, and day five Monastir. Start on a Tuesday. The archaeological museum is closed on Mondays, and the two big mosques close to visitors earlier on Fridays, so the order puts the mosque day (Kairouan) on a Wednesday and the open-air day (El Jem) on the Friday. If you're also doing the capital, Tunis is 140 km north, and the Tunisia country page has the basics on language, food and money.