Their lawyer said more passengers were expected to file suit over the coming week.
"For the physical stress alone, the claim is €2,500 in compensation per person," attorney Hans Reinhardt said on Saturday.
Eleven people have now been confirmed dead after the Costa Concordia hit rocks and sturned over near Italy's Giglio Island on January 13. It is thought that 12 Germans are among the more than 20 people still missing.
Police are investigating the ship's captain, Francesco Schettino, on suspicion of manslaughter and abandoning the ship before passengers were safely evacuated.
Five German passengers, including two married couples and one woman from the state of North Rhine-Westphalia, are suing the cruise operator for damages of around €100,000.
"Jewellery, credit cards, important documents – after an accident like this, it's all gone," the lawyer said. Passengers normally have to four weeks after the end of a trip to file a claim.
A new poll conducted by the Emnid institute for the weekly Bild am Sonntag newspaper indicated that 51 percent of Germans had ruled out taking a cruise because of the Costa Concordia wreck.
German Transport Minister Peter Ramsauer is now looking to push through new safety rules for large cruise ships.