USA:

U.S. Citizenship and Immigration Services
h**p://uscis.gov/graphics/howdoi/renew.htm

What is a Permanent Resident Card?

A Permanent Resident Card, commonly known as a Green Card, is evidence of your status as a lawful permanent resident with a right to live and work permanently in the United States. It also is evidence of your registration in accordance with United States immigration laws. The Permanent Resident Card is also called Form I-551.

Welcome to Florida
h**p://www.ukflorida.com/index.htm

FAQ
h**p://www.ukflorida.com/faq.htm

Why Is It Important to Renew an Expiring/Expired Card?

Lawful permanent residents with an expiring/expired Green Card will not lose their legal status in the United States–their lawful permanent resident status will not expire or change. However, they will need to renew their expiring Green Card in order to maintain acceptable evidence of their permanent resident status and avoid possible difficulties in obtaining employment, benefits, and re-entry into the United States after traveling abroad.

Green Card Renewal
h**p://www.refugeesusa.org/news/leg_updates/991210.pdf

(....) Please remind clients that expired green cards do not effect status, and that they will be not be deported or refused admission for not having a current green card.

Every ten years the GC should be renewed but already after 5 years one can apply for the american citizenship.


Germany:

The maximum duration for the german GC is 5 years.

After 8 years as a lawful permanent resident one is allowed to apply for the german citizenship.

Conclusion: It was highly unfair to call the german card the same way the american Green Card is called. It was sort of a german lie.

Why did nobody tell before application?

You are right.. name "Greencard" is misleading but this was clearly stated in the brochures of Arbeitsamt etc.. that "German Greencard" was limited to 5 years..
so I think they have already said that before application.. (at least we can not blame them in this manner)
BUT, most people had the hope of extension or PR after 5 years.. that is another point.. :-)

Regards

Lacrima