Final answer:
The Fifth Amendment allows governments to enforce controls over private land through eminent domain, requiring 'just compensation' for the property owners.
Step-by-step explanation:
The amendment to the U.S. Constitution that allows governments to enforce controls over the use of privately held land is the Fifth Amendment. This amendment guarantees "Life, liberty, and property," and includes a provision known as the Takings Clause. The Takings Clause acknowledges the power of the government to exercise eminent domain, which is the authority to take private property for public use, as long as the government provides "just compensation" to the property owners. The Fifth Amendment strikes a balance between the need for public good and the protection of private property rights.