Agree with Mrs Guy, Passo is a great choice, and with Kiwinyc, Monterosa is a good choice too - bearing in mind that also Toddmummy is spot on, transfers can be terrible.
I would not drive to Italy. Snag a cheap flight, offset it if you want. Re yr five year old, shd be fine to start skiing; we started youngest DS at almost-four, but he is a big lad.
Italy is great for a few reasons: first, the only REALLY busy times on the slopes are weekend mornings. Italians see coffee-sipping and testing new sunglasses as equally important activities as skiing so afternoons, and weekdays, can see empty pistes. Second, the well-known family orientation and the likelihood of the DCs enjoying the food. Third, as pointed out, cheaper than most other serious winter destinations (Austria, France and Switzerland).
Here's a list of family-friendly resorts I found:
Great family resorts:
Les Gets - dedicated pistes, friendly
Laax - Ami club for littl'uns
Meribel - abundance of childcare options
Aspen - Buttermilk ideal for new skiers
Cortina - traditional, and great kids deals
Passo Tonale - Italian welcome for kids, value
Levi - two words: Santa Claus
Are - good snow, waterpark and dog sledding
Adelboden - quiet, with lots of piste (185km)
El Tartar - Andorra's best family resort
Ellmau - gentle slopes, classic Austrian village
Ste Foy - quiet, enclosed area with good links
Family-friendly operators
Scott Dunn
Ski Famille (Les Gets)
Esprit Ski
Ski2 (Italy)
Skibizz
Family Ski Company