Travel from cinque terre to Kastelruth

4 hours by car? Really? Is that with one of those cars that can be converted into an airplane?
6 hours might be possible if you have the car in hand. But why have a car in the Cinque Terre.
If you want to do that, rent a car in La Spezia, which will take a bit of time. Keep in mind 30 euro worth of tolls.
It comes out to a wash time wise, but your choice.

I was using the rome2rio application for the 4 hour estimate. Assuming by the response that is inaccurate.

Four hours by car seems a little tight to me, too. One thing about driving: the driver, and possibly the navigator, may not see as much as both would see on a train (eyes on the road or the map, unless you pull over frequently, which adds time to the trip).

www.viamichelin.com says 5 hours from La Spezia, where you can pick up a rental car. Mostly autostrada except for a short cut between Parma and Mantua. Keep an eye out for robocam speed traps.

One of the shortest trips by train from the Cinque Terre to Bolzano is 6H:11M, with 3 changes. Two segments will be via Freccia high speed train, so those will be faster than by car. Kastelruth / Castelrotto doesn't have train service, so you'll need to take a Bus from Bolzano. The trip is about an hour as I recall. The details are in the guidebook but if you need more information, post another note.

When using either public transit or rental cars in Italy, there are a few potentially expensive "caveats" to be aware of. With rental cars, you'll need to have the compulsory International Driver's Permit, which is used in conjunction with your home D.L. You'll also have to be extremely vigilant to avoid the dreaded ZTL (limited traffic) areas, as expensive fines will result for each pass through one of these areas. There are also tolls, automated speed cameras, parking costs and expensive fuel costs (I believe it's about US$6.35 a gallon at the moment).

Thanks ken. Is there a website specific to the high speed trains? That sounds like a better idea than driving.

www.trenitalia.com is the Italian railway site.

I don't see why it should take 6 hours from La Spezia to Castelrotto, unless you include a long stop for lunch. It's 400km (250 miles) from La Spezia to the Bolzano Nord exit. It's 100% autostrada because the fastest route is to take the A1 south between Parma and Modena, then the A22 north to Bolzano. The speed limit is 130km/h (81 mph) the entire segment. Even if one drives at an average of 100km/h (60mph), so well below the limit, it will take about 4 hours to Bolzano Nord. After you exit the freeway there are another 20km (12 miles) to Castelrotto on the Provinciale. I've driven that road and you can drive comfortably at 60km/h. Even if one drives more slowly, in half hour after the freeway exit you are in Castelrotto. Therefore the total driving time can't be more than 4.5 hours. Frankly having a car up there it's a good thing to have and renting it in La Spezia will probably save time and maybe money depending on whether one travels alone or with two or more people.

Renting a car as Roberto recommends in La Spieza makes the most sense to me.
it would definitely be faster than a train with 3 stops and then an hour bus ride, factor in schedules and it will not even be close.
And then you are stranded in Kastelruth with no car plus what do you do to get to Venice in May? Another longer trip than if you had your car from La Spieza and dropped off in Piazzale Roma.