Some points missing

First of all, 5th Amendment was intended by the framers to be applied only to the federal government, not the government of several states. All eminent domain cases challenged on the 5th Amendment ground were rejected and by then eminent domain was pretty much a local matter governed by state law and state could take without any compensation. This was the case until the Supreme Court found a way to apply 5th Amendment through the 14th Amendment Due Process of law guarantee. Chicago B. & Q. R.R. v. City of Chicago

Second,the 5th Amendment to the Constitution says "nor shall private property be taken for public use, without just compensation." This is a recognition of pre-existing power of the federal government and the governments of the several states, not to grant a new power. Which means, taking private property for public use is power guarranteed by the Constitution, as long as the government provides just compensation.

Third, the Supreme Court made it clear that the legislative power of taking was a Constitutionally guaranteed power that the Court must defer for separation of power considerations. In Hawaii Housing Auth. v. Midkiff, the Court said "When the legislature's purpose is legitimate and its means are not irrational, our cases make clear that empirical debates over the wisdom of takings . . . are not to be carried out in federal courts." The court made it very clear that the correct standard of review under 14th Amendment Due Process Clause and Equal Protection Clause should be rational based. Means, as long as the taking statute enacted by state legislature to take private property for public use is for a rational state purpose, it will be upheld. Even though property right is considered a fundamental right, for separation of power concerns the Court will not invalidate these statutes. In this vein, the statutes will be presumed constitutional and the one challenging it must bear the burden to prove that it is not rational. Sometimes the courts will find the rationality themselves. To illustrate how easy to find a rationality, there was a case in which the California statute criminalized adult men having sex with underaged women as statotry rape, but not adult women having sex with underaged men. The Supreme Court upheld the statute on the reason (by California) that the state interest was to prevent underaged pregnancy. If procedural due process is violated, such as government takes without hearing, that is a valid case in the Supreme Court.

Finally, most people know that no two properties are the same. Unlike commodity like a car that one can find a fair market value, a house, on the other hand, will be difficult to find fair market value. To determine fair market value often involves intensive hearing, expert opinions, and things as such.