Rome-Venice-Cinque Terre

Hi, I'm coming to Italy at end Apr - early May.
I'd like to do Rome, Venice and Cinque Terre, probably flying into Rome. After that I'm flying to Amsterdam. How many days would I need for each city? I'm travelling with my mum who is 65 yrs old, so preferably not too hectic of a journey. I don't need to see ALL the sights in every city, but I do want to visit all three places and at least experience the vast difference in the cities. Also, what should my itinerary be? Is it better to do Rome -> Cinque Terre -> Venice -> Amsterdam? or otherwise? Would love to hear some advice...thank you!!! Joyce