The nearest airport to Interlaken is Zürich. 2h10 from Zürich airport to Interlaken by train. If you fly, you would also need to get a train from whichever of the Cinque Terre towns you are staying in to the airport (Florence?). Swiss flies from Florence to Zürich
The alternative is train all the way. This would take 7-8 hours,. You can look up train times on the Swiss railways site: https://www.sbb.ch/en
Sample train timing:
Monterosso dep 07:29, Levanto arr 07:33
Levanto dep 07:59, Milano Centrale arr 10:55
Milano Centrale dep 11:23, Spiez arr 13:53
Spiez dep 14:05, Interlaken Ost arr 14:28