sarah.
First of all, congratulations! I believe the Italian equivalent is Tanti Auguri.
Your profile doesn't indicate where you're flying from, so I assume you've allowed for two flights days. You'll generally arrive in Italy the day after you depart your home airport, and one day will be required for the flight home.
My suggestion would be to leave your Itinerary as it is. A few thoughts......
While your time in Venice is short, it will allow a quick look and you can come back and explore further on a future holiday. I'd suggest leaving the Cinque Terre at four nights, and also make Rome four nights (the most time possible is always better). Spending four nights in the C.T. will allow three full days of touring. You may need a few days at a more relaxed pace after your stays in Venice and Florence, and the C.T. is a great place for that. You can do some hiking, tour the five towns and Porto Venere, and of course enjoy some great Pesto in the area where it was invented. You'll probably have to endure the cruise ship hordes from about 10:00-16:00, but if you're out touring during the days that may not be much of a concern.
For your stay in the Cinque Terre, Monterosso is a great choice as there's a good selection of wonderful hotels there. Depending on your budget, you could look at.....
It would be a really good idea to get something booked NOW, as hotels fill up quickly.
In order to use your sightseeing time most efficiently, it would be a really good idea to pack along a copy of the RS Italy 2019 guidebook. The book has information on various sights, how to minimize time waiting in queues, restaurants, etc. (los of very useful information). If you're travellling with an iPad or whatever, it's also available as an E-book in several formats.
I assume you're planning on getting around mostly by train. If you haven't used trains or other public transit in Italy, there are a few potentially expensive caveats to be aware of. If you need more information, post another note here.
Don't forget to pack along some Money Belts, as there will be pickpockets!
Buon Viaggio!