Lugano is Switzerland with the volume turned down and the Italian turned up. The town sat between Como and Milan for centuries, passed to the Swiss in 1513, and only became part of the canton of Ticino when it was created in 1803. You can still tell. The language is Italian, coffee comes in a small cup at a bar counter, lunch lasts as long as it needs to, and the prices are fully Swiss. In the 1960s and 70s money from nearby Italy turned the city into Switzerland's third financial center, which explains the number of banks next to a lakefront lined with palms.
The reason to give it five days is that Lugano is a very good base. Two funiculars lift you out of the city in minutes, the lake has a fishing village on each side, and a train takes you to a UNESCO fortress in 15 minutes, to Locarno in half an hour, and to Italy in about 40. Be honest with yourself about the price: this is Swiss money, so a lunch is around CHF 25 to 35 and a funicular return is CHF 26 to 32. The Ticino Ticket, which partner hotels hand out, makes the trains and buses free.
The plan keeps each day in one slice of the region. Day one is the old town and the lake, day two Monte Brè and the walk to Gandria, day three Morcote and Monte Generoso, day four Bellinzona and Locarno by train, and day five the Verzasca valley. Start on a Wednesday: the museum hours work, and day four lands on Saturday, when Bellinzona's market is on. Nearly everything with a lift, a boat or a garden is built for April to early November, and by early November the shutters come down. Every stop below says what changes in winter, and there is a short list in the tips. More on the country is on the Switzerland page.