Which Act provided 160 acres of public land free to families that settled on it for five years?

The Homestead Act is the correct answer because it was enacted in 1862 and aimed to encourage westward expansion by granting 160 acres of public land to individuals and families, provided they improved the land by building a dwelling and cultivating crops for at least five years. This act was significant in promoting settlement in the American West, facilitating the agricultural development of the region.

The policy was designed to attract settlers to promote the growth of the nation and support the transition to an agrarian economy. By making land accessible to ordinary people rather than just wealthy landowners, the Homestead Act played a critical role in shaping the demographic and economic landscape of the United States during this period. In contrast, the other acts mentioned do not pertain to land distribution for settlement: the Chinese Exclusion Act focused on immigration regulations, the Mining Act dealt with mining rights and regulations, and the Frontier Act does not refer to a recognized piece of legislation related to land distribution.