Final answer:
The Fifth Amendment's Takings Clause allows the government to exercise eminent domain to take private property for public use if it provides just compensation to the owners.
Step-by-step explanation:
The Fifth Amendment affects this case through its Takings Clause, which stipulates that the government may exercise its power of eminent domain to take private property for public use, but must provide just compensation to the property owners. This means that while the local government can take the land for the new transit station, it must compensate the residents fairly, typically by paying the fair market value of their properties. The amendment does not require the government to pay double the property value nor does it obligate the government to search for alternative sites as part of the eminent domain process.