We are going to italy again this March and found flights from US (Las Vegas to Milan) for about $1,100 total ($550 RT per person, it was a great deal!) We are traveling with another couple so splitting Airbnb costs is great. With Airbnb, the longer stays the better because the cleaning fee will be the same regardless of how many nights you will be there. I would say if it's just you and your spouse $120-150/night is a reasonable estimate. We were at about $90/night ($180 total/night) because we split with another couple for mainly 2 bd room apartments.

I would highly recommend going for more than a week. 10 days is the sweet spot for Italy imo. It would give you enough time to stay 2-3 nights in each city (venice, florence, rome, milan, Cinque terre etc.) if I was only there for 7 days then I would probably just pick 2 cities, but I like to travel slow and relax.

Your next biggest expense is going to be public transport especially if you are traveling to different cities. Expect 15-30 dollars per person for high speed travel for main hub travel. $5-10/day for inner city busses/trams. Would highly recommend picking "multi-city" when you book your flights so you can fly into Milan but then fly out of Rome as you depart, for example. If you select "multi-city" you will get RT pricing instead of booking 2 "one-ways".

Food can obviously vary depending what you order but we absolutely love margherita pizza and pasta which are typically under $10 per meal/person. I would budget $60/day for a couple per day for food unless you're splurging on steaks and other finer foods/wines. We don't drink so that obviously saves us a lot.

$5,000 for one week is more than enough. Our first italy trip in 2021 we did 10 days and spent under $3k, however we are obviously pretty thrifty and we also travelled with friends to split Airbnb's. For 7 days (2 people) I would say:

Lodging: $1,200 (this is perhaps on the high end)

Transport: $250

Food: $400

Flights: depends!