Complex sentence: He joined Cortés' side, and after Narváez was defeated, in Zempoala, Veracruz on May 24,1520, and he participated in the conquest of Mexico.
Split into simpler sentences: He joined Cortés'side, and fought against Narváez in Zempoala, Veracruz on May 24,1520. After Narváez' defeat, he participated in the conquest of Mexico.