Temps in May?

There could be quite a difference between the high temperatures in Venice and Florence/Rome in May. Pack layers. I use a fleece jacket for warmth and a waterproof rain jacket for wet or windy conditions. If necessary, I wear both. On cool days it may be somewhat chilly early in the morning and after the sun goes down if you get caught in the rain, but I wouldn't expect to need a heavy coat or jacket in May in the cities you mentioned.

May is the wettest month of the year in Venice: https://en.wikipedia.org/wiki/Venice

Be careful about depending on monthly averages. They hide highs and lows, and in some cases the averages are based on time periods that exclude recent years.

I think the figure you're quoting from Google may be the average high temperature; even if May 2025 is dead average, you'll only have temperatures like that during the warmest part of the day.

In Italy in May, overall, there is more rainfall in the north than in the south. The temperature is just the opposite, with the south being higher than the north. However, whether it rains or not is not very stable.

you can check the actual weather for May over the last decade or so at https://www.timeanddate.com/weather/@3173131/historic?month=7&year=2023 Just change the city and month to what you want

Temperatures in the 70s F is correct, during the day. However at night or early morning expect temperatures to drop to the high 50s F or low 60s F, therefore you will likely need a light jacket and/or a light sweater for the evenings. Also consider that both Venice and the Cinque Terre are on the water, therefore it is a bit cooler (or less hot) during the day, but at night temperatures drop down less, while in Florence in particular, there is a more marked temperature excursion between night and day. Even on a warm day, I wouldn't say it is likely to be muggy in May. But in the unlikely event it is, it is probably going to be Venice. If your journey starts from Venice, then I would say it is unlikely you will experience mugginess in early May, even in Venice.

Chance of clear skies is a 50/50 chance, while chance of precipitation is, I would say, 25%-30%. May is not the wettest month of the year, but it is not as dry as Jun-Aug either. I would say that during a 3 week stay, it is very likely you will see at least some rain, but consider that in some years May might experience a lot of rain and even cooler temperatures that normal. As such you should be prepared for the possibility of rain. Carry a portable small umbrella or be ready to purchase one. I can guarantee you that minute rain starts to drop, there will be scores of African and Middle Eastern (or also South American) migrants who will magically appear all of the sudden from nowhere ready to sell hundreds portable umbrellas to tourists at an inflated price (bargain hard, and eventually they'll agree to sell if for a handful of euro much lower than the initial offer).

We were there the first week last May. Low-mid 70’s and sunny days.

I was in Tuscany visiting relatives the second half of May 2019. It rained practically every single day and temperatures were in the 60s during the day and high 50s at night. It was like in March.

I was also in Florence (I go every year) the last week of May of 2005, temperatures were in the 90s during the day. No rain. It was like in July.

Be ready for anything, except probably for snow (although it did snow in May in the Dolomites a few times I went, but you don’t plan to visit the mountains). The best strategy is to check the weather forecast for the following 10 days right before you depart.

Plus, early May is typically cool and it warms dramatically by month's end, so you really do need a light jacket. I would expect to be hot during the day and cool at night.

Roberto, actually we WILL be in the Dolomites for 2 nights on this trip, LOL, just after we leave Venice!

Time to dust off those snowshoes then.
Or learn how to say snowshoes in Italian: “ciaspole”

https://www.ursusadventures.it/guida-alle-ciaspole/