a local government has plan to build a new trainsit station on a site where several homes are currently located the residents do not want to move how does the Fifth Amendment affect this case

The Fifth Amendment addresses the process in which the federal and state governments can acquire private property in order to convert it into public use, also known as Eminent Domain. The amendment states the following:

No person shall be ( ...) deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.

So, in the given case, the residents are protected under the 5th Amendment. Before the local government can acquire their property they first have to obtain the permission of the landowner and pay just compensation for their properties.

The case Kelo v. City of New London (Supreme Court, 2005) articulated the principle that a town may use eminent domain to seize private property under the 5th Amendment's "Takings Clause" if the seizure is to benefit the public at large. Since the transit station would benefit the public, it is likely that the 5th Amendment's Takings Clause would apply.