Here are the answers to your questions:
5. **Which of the following is NOT a reason for the rivalry between China and the United States?**
- C. America's resistance to China's free-market reforms
(This option doesn't align as clearly with reasons for rivalry as the others, which are more directly tied to geopolitical and ideological conflicts.)
6. **Which of these events demonstrated China's status as an important member of the international community?**
- A. The 2008 Beijing Olympics
(The Olympics showcased China on the global stage, highlighting its rise as a significant player in international affairs.)
7. **What small island has the potential to spark conflict between China and the United States?**
- C. Taiwan
(Taiwan is a highly sensitive topic in U.S.-China relations and has the potential to spark conflict due to China's claims over the island and U.S. support for it.)