Sicily

If just using public transportation I'd say Palermo would be a bit more convenient. But it really depends on what else you want to see while in Sicily. With just 5 days would probably be best to just concentrate on either East (Taormina) or West (Palermo). Also may depend on how you're getting there - ferry to Messina or flight (Palermo or Catania).

Definitely Palermo!!! Palermo has changed a lot from the city of the '80s and '90s that was rife with graffiti and Mafia influence. It is a charming city on the rebound with great restaurants, amazing architecture and a vibrant street life. Taormina is pretty but after about a day, there's not much to do there other than shop and eat and public transportation from Taormina to anywhere else on the island would be inconvenient at best. Palermo has lots of things to see and do, train and bus connections to just about everywhere on the island (albeit it will take a while as public transportation lags behind the mainland). We stayed at the B&B Delle Vittorie in Palermo. It is located just off via Maqueda, a pedestrian street full of shops and restaurants, very close to the opera house and within walking distance to everything in central Palermo. The accommodations are lovely, the breakfast is delicious and the host/owner is very friendly and helpful. They will also store your bags if you arrive early or leave late after checkout time. You do NOT want a car in Palermo, but a car is the most efficient way to see the rest of the island. If you are set on driving, may I suggest staying near Siracuse (island of Ortygia) in southeat Sicily. It is easier to maneuver by car in the Siracusa area (the traffic and parking situation are way easier!!!). Also there are lovely cities to see in this part of Italy - Ragusa, Noto, Modica, as well as Ortygia. In this case, you would fly into Catania rather than Palermo. If you are flying into Palermo, you can visit Cefalu, Monreale, Segesta, Erice, perhaps Trapani. But honestly you can spend five days in Palermo and still not see everything. We spent four days in Palermo before doing the 10 day RS Sicily tour and still didn't get to do everything we wanted to do in that city.

Palermo!

A second option if you don’t want Palermo, could be the Ortygia section of Siracusa. Plenty to do in Siracusa, lovely seaside feel in Ortygia, and good day trip options - Ragusa, Noto, Etna, beaches, Catania (not sure how convenient public transit is for the day trips, though).

Sicily has so much to see and five days is not a lot of time. I think you will need to decide whether you want to focus on east or west. You can travel by bus or train on either side of the island. I did a 22 day trip all around the island in September mostly depending on public transportation. If you are not afraid to drive, that would be the easiest, but you really won't need a car in the cities and if you get one make sure you are fully insured.

What are your interests? Do you want to see ruins? Churches? Scenery? Food? Architecture? All of the above? One of the forum members recommended that I view the three part documentary titled “Sicily Unpacked” prior to my trip. It is available on youtube.com. It follows an Italian chef and a British art historian on their travels around Sicily. Excellent and gave me lots of ideas for places to visit. You haven't mentioned the time of the year for your visit. Summer is very hot and sunny. Even September to early October was very hot on my trip. Choose spring or fall.

I think I personally would choose Palermo as a first time visit base. Lots of sites to see in Palermo and Palermo is very walkable. A must see would be nearby Monreale and maybe a visit to Segesta to see the Greek and Roman ruins and possibly combine that with a visit to beautiful Erice. Another daytrip could be to Cefalu. Cefalu is an easy bus or train ride away and is such a pretty town to stroll around and explore. Monreale can be reached by bus. We hired a private driver for a day excursion to Segesta and Erice and to see the salt pans outside of Trapani/Marsala.

If you want something more off the beaten path take a look at Mazara del Vallo, a lovely smaller fishing town with lots of Tunisian influence and a historic center full of narrow streets and alleyways. We took the train from Palermo to Mazara del Vallo. It involved one very easy change of trains. I learned about this town from the Sicily Unpacked videos. From Mazara you can take the train and then a local bus to the magnificent ruins of Selinunte. It is not very far away. We did it as a daytrip and returned to Mazara. I actually enjoyed visiting the ruins of Selinunte more than those of Agrigento. (Both are wonderful but Agrigento was so crowded and Selinunte was almost empty and its location right next to the sea was stunning.)

If you choose the east I would base in Ortygia. It is beautiful. From there you can branch out to the baroque towns or to Catania (I very much liked Catania) or a daytrip or overnight to Taormina. Be prepared for hordes of tourists in Taormina.

I was very pleased with our BnB choices for Sicily. Send me a PM once you decide what towns you are going to and I will be happy to give you the names of the places we stayed. I was in Palermo in 2013 and again in 2019 and saw a big change in just six years as to cleanliness, ease of getting around, and attention to tourism.

Hope this gives you some ideas you can use.

At this point I can only speak to Eastern Sicily. In 2014 we were on a Southern Italy and Sicily Tour. Our group started in Taormina, Mt Etna. After the tour we went to Siracusa 4N (per train) and day tripped to Noto, Ragusa, Modica and Catania (1N). We knew we would return to see more! That said, we are returning (self guided) next fall for 28N. We will be starting in Palermo and ending in Catania. We will be revisiting some of our favorite places as well. We are following "Priscilla's route" see her forum trip report "My trip to Sicily-in Zoe's memory" using public transportation (bus, train)

We too will be staying at the recommended B&B Delle Vittorie in Palermo. In Ortigia we will be revisiting the charming B&B La Via Della Giudecca.

Like mentioned up thread choose what sparks your interests! We found the RS Sicily Guidebook and Lonely Planet very helpful.

I vote Palermo. In addition to places to see in the city, it’s easy to get to Trapani/Erice, Cefalu, Monreale, and Segesta.

My answer would depend on what you wanted out of the trip.

Home base for what? Do you want a big city or a smaller one? Are there specific day trips you were planning from your home base?

I liked both Palermo and Taormina, but many seem to feel Taormina is too packed with tourists. I felt that the atmosphere in Taormina was so special that even the crowds couldn't ruin it. However, I was staying at a relatively fancy place above the center of town, and I think that had a great, positive impact on my visit.

Here's my complete and detailed Sicily trip report review, including information about where I stayed in Palermo and Taormina: https://community.ricksteves.com/travel-forum/trip-reports/sicily-palermo-caltanisetta-siracusa-taormina

If you mean 5 nights, which is 4 full days, without a car Palermo may be your best option if you want sightseeing. With a car, Ortigia is best for sightseeing - visit Catania/Mt. Etna, Ragusa/Noto, even the Roman villa outside Piazza Armerina, and Taormina.

Sicily requires a minimum of three bases, four is better.