I'm a little confused, why can't you rent the car somewhere close to your base in theCinque Terre, such as La Spezia?
The journey breaks down into 3 parts, which depend on whether you go via Milan (and ignores mention of Pisa).
via Milan
the first bit is a mix of coasts and hills, the middle bit is a dash across a plain with industry and Milan, followed by some staggering mountains and the Stelvio Pass - which you will be too tired to enjoy unless you stop the night north of Milan.
not via Milan
you cut across the Appenines on some reasonably interesting roads, dash around Parma and across the plain towards Lake Garda then work your way up with the scenery getting better. This should be OK in a day, even if you have the delay of picking the car up and doing the paperwork.
OK, I summarised them but this is a signficant haul.
Also, 5 people? all adults with luggage? You will struggle to get them into one car unless you go for something like a Mercedes E class or bigger. You'd really need a small mini-van, something like a Mercedes V class or VW Caravelle.