Arezzo to Cinque Terra

Arezzo is far from the Cinque Terre.
You will likely need 4 trains to get there (maybe 3 if you stay in Monterosso):
1 - AREZZO > FLORENCE
2 - FLORENCE > PISA
3 - PISA > LA SPEZIA
4 - LA SPEZIA > CINQUE TERRE

That is a 4 hour trip.

I don't know where you are staying, I presume somewhere near Arezzo, but if I had a rental car somewhere near Arezzo, I would drive to La Spezia and then take the train from there. There is a big parking structure at the La Spezia train station where you can park securely for days. Monterosso and Riomaggiore have parking as well, if you are staying in one of the two.
You can drive from Arezzo to La Spezia in 2.5 hours. You save at least 1 hour and above all getting off and on trains with luggage multiple times.
But the best thing to do is to time your trip to the Cinque Terre at the end of your rental car period, and return the car to La Spezia, then continue the rest of your Italy trip without a car.

lisa,

You can find ticket info on the Trenitalia website. That particular journey will likely use a combination of Regionale and "fast" trains, so best just to buy tickets in Italy, either from a Kiosk or staffed ticket office.

Were you planning to do this as a day trip, or spend a few nights in the Cinque Terre? If you want to arrive early, there's a departure from Arezzo at 06:32, arriving Monterosso at 10:06 (time 3H:34M, two changes at Firenze Campo di Marte and La Spezia Centrale - the middle segment is via FrecciaBianca, so compulsory reservations which will be provided with the ticket - the other two segments are via Regionale so DON'T forget to validate the tickets prior to boarding the train on the day of travel, or you'll risk hefty fines!).

There are numerous other departures throughout the day. Check the Trenitalia website for all the details.