Could you elaborate on the question, "Which country is 5000 years old?" It's an intriguing inquiry, but it's worth noting that countries, as political entities, are relatively recent phenomena in human history. However, if we're considering ancient civilizations and their cultural or political continuities, several regions have histories stretching back several millennia.
For instance, Egypt, with its rich pharaonic civilization, can be traced back over 5000 years. China, with its continuous civilization since the Neolithic Age, also has a similarly lengthy history. Mesopotamia, the cradle of civilization, encompassing present-day Iraq, Iran, Syria, and Turkey, boasts a rich history spanning more than 5000 years.
So, to answer your question, it's not so straightforward to pinpoint a single "country" that is precisely 5000 years old, but several ancient civilizations have histories that extend back that far or even further. Is there a particular aspect of these ancient civilizations you're interested in exploring further?