Italy itinerary in mid September this year for 5 nights, 6 days

You have way too many destinations. In 5 days, you will be hard pressed to see even two destinations. If you focus on Rome, you will have a short but enjoyable visit, and you will be able to see the ancient sites and also the Vatican, including the Vatican museum. If you really need to see a second destination city, I suggest Florence, which is not that far from Rome by train.

If you fly open jaws into Rome from Switzerland and then depart from Florence, your trip will be rushed but enjoyable. Don't even try the Cinque Terre or the Amalfi Coast with your limited time. Venice is a bit of a slog from Rome, leaving you little time to enjoy the city before departing Italy. With fewer than 3 days in Venice, I wouldn't even consider Burano.

Thanks @webfy1 !

Yeah, we are confused between Florence / Venice. Whatever we choose we plan to reach either Florence / Venice by train from Swiss by 2-3PM on our Day 1 to Italy.

Plan to spend two nights there and leave for Rome to see rome and vatican. Cinque terre and Amalfi coast looks really amazing to us and that's why we were thinking to spend some time there too but with limited no of days we are really confused.

Do you think can we visit Rome, Vatican, Amalfi in 3 days?

I really don't think that's possible. Amalfi is an outlier, a place that is difficult to get to under the best circumstances. Figure 3 1/2 to 5 hours from Rome each way, and you are traveling a long way for very little reward. Up to you, but if this is a vacation, rather than a marathon, then you will want some time to relax as well.

Edited to say that it is POSSIBLE, but I wouldn't want to make the trip in that limited number of days.

Sorry, my bad we will have 6 days and 5 nights.

Day 1, 2 PM - Florence hotel check-in, lunch till 4PM, 4-8PM local sightseeing.
Day 2, Early morning leave to Cinque terre and reach by 11AM, 11AM - 8PM in Cinque terre, return or stay there only.
Day 3, Florence local sight seeing and overnight stay.
Day 4, Checkout and leave early morning for Rome, reach Rome by 12 AM, lunch and hotel check-in by 2PM. Visit some ancient sites today.
Day 5, Vatican museums and city.
Day 6, Hotel check-out, visit Colosseum today or some other place if possible and start for Airport. Flight at 9PM.

Does this looks doable or should we cut Cinque terre too?

I would choose 1 location in addition to Rome for your time.
Since you are coming from Switzerland ; Florence is probably easiest logistically but if you would rather see Venice than Florence go with that.
2-3 nights in your first stop (Florence or Venice)
3-4 nights in Rome
no time for anything else.

You also need to do a lot more planning. Florence is a lovely city, but most of the museums are not open in the evening. And the top museums have either very long lines (over an hour), or you need to buy tickets in advance. That's also true of the Vatican Museum. Your ambitions are going to lead to a lot of disappointment if you don't plan (sorry ... ) and research more carefully. That is, I'm saying your detailed military schedule is actually not helpful, since the attractions don't know anything about it!

There are plenty of casual places to eat in Florence, but it's hard to get into real restaurants in Italy in the middle of the afternoon. If you are just a little late for your 2PM hotel check-in, you may be limited to pizza or sandwiches for lunch. I haven't been to Florence in a while, but I've been to Italy several times.

Did you give the month and year of the trip?

Its September end 2018, 20-25 September to be precise.

Agree we have to plan more, but we need to close on our places first i.e. amongst Florence / Venice and then plan accordingly.

Yes, first decide between Venice or Florence. There will still be quite heavy crowds in both cities for your dates. With your very limited time, you don't have time for more than 2 places. Forget CT or AC for this trip. There are very few museums, galleries or churches open in the evenings in Florence, so plan accordingly and buy tickets in advance. For Rome, also plan your days with opening/closing hours in mind and buy tickets for the Vatican and Colosseum in advance.

Its September end 2018, 20-25 September to be precise.

It's already August and you haven't figured out your itinerary yet? ...you're setting yourself up for disaster. Italy (along with France) is flooded with tourists right now. Every popular destination is jam-packed, lines are measured in hours. Tickets are bought in-advance...or, you wait in line; add in the heat and hunger...not exactly a good way to enjoy a vacation.

With just 10-days of travel, you're best staying in one country. However, you're flying into Switzerland and flying out of Rome...you should spend your remaining time in Rome. Enjoy your time there instead of a death march of pack/unpack, grab train/get-off train, drag luggage on accommodation search every-other day. Eliminate Florence, Venice, CT, Amalfi.... you can visit them on your return trip when you have more time.

or should we cut Cinque terre too?

Yes, cut it out.

Go to Florence and Rome. Venice, Cinque Terre, and especially the Amalfi coast are too much out of the way. I would suggest 2 days in Florence and 3 days in Rome. That should be enough time to get to the highlights of each city. As others have mentioned, be diligent in making your plans for tickets and museum visits so that you aren't left outside looking in after closing.

Make sure you give yourself plenty of time to travel to the Rome airport and pass through check-in and security at the airport, well before your flight time.

What are your plans for your 4-5 days in Switzerland?

I would either skip Cinque Terre in your detailed itinerary days, or do this option. Personally, I like the contrast of Venice/Rome more than Florence/Rome and would save Florence for a future trip when you can also include Tuscany small villages, Cinque Terre, etc.

Day 1, afternoon check-in at Venice. Explore Venice.
Day 2, see St. Mark’s as soon as open. Accademia Museum late afternoon, go to San Marco piazza in the evening after day-trip tourists have left. Spend time away from the Rialto-San Marco route during the day; it’s overcrowded.
Day 3, boat to Burano and/or Murano. Attend an opera at La Fenice?
Day 4, Checkout and leave early morning for Rome, reach Rome by 12 AM, lunch and hotel check-in by 2PM. Visit some ancient sites today.
Day 5, Vatican museums early AM; other sites mid-afternoon, etc.
Day 6, Hotel check-out, visit Colosseum today or some other place if possible and start for Airport. Flight at 9PM.

Both Venice & Rome have wonderful ambiance in the evening. Eat a late dinner, and enjoy walking around the sites. The Pantheon in Rome is gorgeous at night, especially with a gelato in hand!

If you don’t have a RS Italy book, pick it up immediately. There’s so much that you will wish you had known to maximize your time before arriving at these cities.

Thanks for your suggestions !

Yeah we know we are running quite late in planning but we want to close it asap. As this is our first travel in both countries and we don’t want to miss worthy places so we are taking too long in deciding and in a group of 4 everyone have their own preferences.

Regarding switzerland - we are staying 2 nights in lucerne and 3 nights in wengen

Is the main attraction in Switzerland the Alps? We're going to Italy next month and were planning to go to Lucerne & then on to Innsbruck, but after our hotel in Lucerne had a fire and our room was cancelled, we cut those 2 countries out all together and now we're going to the Italian alps. I think it was a blessing in disguise.

----------Regarding switzerland - we are staying 2 nights in lucerne and 3 nights in wengen

We stayed in Wengen last June - beautiful!! Only problem we had was that a train had derailed going down the mountain when we were leaving, so we had to go up and over. Made our connection in Lucerne by 30 seconds! Next time I'll stay on the valley floor the last night.