CT or Milan first ?

My thought is shorten Milan, go to 5 Terre, then to Florence, then to Venice. Much more direct IF you are going to Florence.

If not, it is easier to get to Venice from Milan.

First, where are you flying out of? That makes a big difference in the order you visit cities.

Second, why 5-6 nights in Milan? To me, one is enough. Spend your nights in Lake Como, Turin, and/or Florence instead of wasting travel time in a day trip to get there. Lake Como and Florence deserve at least 2 nights themselves. Never been to Turin so can't respond.

I would give Venice 2 or 3 nights.

The only night you need in Milan is the one before your flight back (if you fly back from Milan).
Upon arrival go straight to the Cinque Terre, if that is what you want to visit. Then Florence, then Venice, then the lakes (Garda? Como? Maggiore?) then fly home. Spend 2 or 3 nights at each location, if you have the time.

I'd agree with the others that 5-6 nights in Milan are too many. You are also very late for booking accommodations in the CT for this July: they book up months in advance.

I'd go directly to the place you can find rooms nearest the CT on your first day, and then Florence, Venice, the lakes (if there's time) and back to Milan for your last night.

We are flying from San francisco. We were thinking of making Milan as a home base so we do not have to pack and unpack . We will stay separate nights in village close to CT and then separate night in venice. Just trying to figure out to start our trip in CT or Milan ( doing sidetrips first). Thanks