Final answer:
The statement is TRUE as Spain's influence before the Spanish Colonial era included territories such as California, Arizona, New Mexico, and Mississippi, which later became part of the United States.
Step-by-step explanation:
The statement described in the question is TRUE. Before the Spanish Colonial era, Spain's influence in North America did indeed include territories that encompass present-day California through New Mexico and Mississippi. During the Spanish conquest and colonization period, territories such as California, Arizona, New Mexico, and Texas were part of the Viceroyalty of New Spain, whose capital was Mexico City. The Spanish established settlements and missions in these areas, which held similarities to their colonies in Central America. The legacy of Spanish control over these parts of North America is still evident today in the cultural influences that remain in these regions. It is also important to note that as a result of the Adams-Onís Treaty, the United States gained the territory of Florida from Spain, indicating the fluctuating borders and control over these lands during historical treaties and exchanges.