MIAMI, Fla.—China’s broad history of 5,000 years isn’t one that everyone is familiar with. For David Weinstein, an investment banker and resort owner, it wasn’t difficult to see the value in Shen Yun Performing Arts because he knows exactly what China has been through and what has been destroyed since the Chinese Communist Party took over. “I think that 100 million people have died from communism. Japan still has what it had, but China is losing what it was. And if you don’t do something, it will be gone forever,” Mr. Weinstein said. “So it’s important.” New York-based Shen Yun’s mission is to revive China’s 5,000 years of civilization. Audience members often comment on the energy they feel from the performance. “I think that when you bring the energy down from the heavens, most Americans don’t understand that in ancient China, there was a very spiritual and divine relationship with …