Travel from Italy to Germany??

Going from the Cinque Terre to Germany by train is going to take you a whole day and it's not necessarily cheaper than flying.

You should look into flying from Pisa, which has flights to Munich (Lufthansa-operated by Air Dolomiti), Frankfurt (Lufthansa-operated by Lufthansa Regional Cityline), and Frankfurt-Hahn (Ryanair).
Both Frankfurt International Airport and Hahn are close to the Rhine. Hahn in particular is not far from Bingen, on the Rhine road where you can catch a boat along the Rhine to Koblenz or Koln. You can reach Munich by train from wherever you are in that area. It's not a short train ride, but probably just as fast as flying once you take into account everything that air travel entails (security checks etc.).

The closest airports to the CT are Pisa, Genoa, and Florence. Use http://www.skyscanner.com to look at flight options.

If flights to Munich don't work, consider starting at the other end of the Romantic Road by flying into Frankfurt. But beware of Frankfurt Hahn airport; it's not near Frankfurt at all. You want FRA, not HHN.

Edit: cross posting with Roberto, who, as expected, gave a superb answer!

Just try requesting train schedules at http://reiseauskunft.bahn.de/bin/query.exe/en. For instance from Vernazza to Munich, the shortest option is 11 hours with 3 connections. There also is an overnight train from Milan to Munich, and you can find that better by searching for it separately.

Thanks so much, everyone!! :)