Final answer:
Jane Jacobs and the Greenwich Village community opposed the 5th Avenue extension because it threatened the communal and historic aspects of their neighborhood. Their activism was successful in preserving the character of Greenwich Village.
Step-by-step explanation:
Jane Jacobs and the Greenwich Village community objected to the 5th Avenue extension because they believed it would disrupt the fabric of their neighborhood. The plan, spearheaded by urban planner Robert Moses, aimed to overhaul parts of New York City through large-scale projects that often did not take into account the existing community networks and the human scale of city life. Jane Jacobs, a noted urbanist and activist, led the charge in advocating for a community's role in city planning and preservation of neighborhoods. Her efforts were eventually successful in stopping the 5th Avenue extension, preserving the unique traits of Greenwich Village.