"China" or "Middle Kingdom" as it's called in China, was historically a fairly vague concept. It was popularized in the 20th century by Sun Yat-sen to refer to the 56 ethnic groups the republic inherited from the Qing empire (Han, Manchurian, Mongolian, Tibetan, Uighur being the major ones).

The 5000-year history refers to the lineage of Han culture in particular. For example, in Japan where most if its Sinic influence was before the republic, Chinese medicine is called Han medicine (Kampo 漢方), Chinese writing is called Han script (Kanji 漢字).

http://en.wikipedia.org/wiki/Chinese_nationalism

I believe when people describe to China as young, they are either referring to the 1911 republic, the 1949 republic, or the 1978 reform.