I've spent a total of 2 weeks in Venice, 6 weeks in Florence, and maybe 4 weeks in Rome (with only 3 half-day trips in the entire time), and would happily return to each for many weeks. I do know what people mean when they say such-and-such a place is only worth a few days, but I don't really understand it. Your list of what you like to do is just like mine, and all three places are superb for all that.
Here's what I would do if I were you. Make some kind of a realistic list or even a schedule of what exactly you want to see and do in each place --- maybe you'll find that you COULD take a day from one place and add it to another. I don't see any way to decide this in the abstract or based on what other people like or don't like. Make sure that you are staying in a neighborhood that you like in each place and in an apartment or B&B or hotel that you like --- nothing turns you off about a place as the wrong neighborhood for you or a bad night's sleep.
Likewise, how do you feel about crowds of tourists? You are going to Italy at an EXCELLENT time of year, but these three cities will still be very crowded at the sights that most people go to see. Not everywhere, just those main sights. If you only go to those sights, you will think Rome, Venice, and Florence are awful. So, you strategize.
People on this forum can help you do all this, once you have some specific ideas of what you want to do. My very first question on this forum was very specifically about riding the electric buses in Florence and I got great advice.
My thought about the 5 - 5 - 5 plan is that it is probably fine. Venice is the one that's the least likely you'll be able to easily return to (it's not a hub like Rome and Florence are, and it's way out to the northeast), and so 5 days there will mean you have really seen Venice pretty well. If you love it, you can return. If you saw and did what you really wanted to see and do, you can feel at peace about not returning.