Do NOT book two one-way tickets...you can do a roundtrip that arrives in one city and departs another. This is very common.

Florence is somewhat crowded at all times of the year, in my experiences. Nothing special happening in May, but the wealth of museums and being in the heart of Tuscany attract a disproportionate number of visitors (including students from all over Italy and the rest of Europe) for how large this city is...

Please limit yourself to only three cities. You will be much happier. Two is even better so that you can take in sights and get to know a couple of places really well, yet feel somewhat relaxed in the evenings for dinner and afterwards, and not be thinking about packing and leaving at the crack of dawn. TRUST ME!