Article V is not the exclusive means to amend the Constitution for the following reasons.

1. Article V text. Article V does not say it is the exclusive means to amend the Constitution. The amendment power is phrased positively: …Amendments…shall be valid…when ratified by the Legislatures of three fourths of the several States. Or by Conventions in three fourths thereof…. The Constitution does not explicitly prohibit the people from designing new amendment procedures.
2. Contrast with precedent. In contrast, Article XIII of the Articles of Confederation explained the process of amendment and explicitly prohibited other procedures. And the Articles of this Confederation shall be inviolably observed by every State, and the Union shall be perpetual; nor shall any alteration at any time hereafter be made in any of them; unless such alteration be agreed to in a Congress of the United States, and be afterwards confirmed by the legislatures of every State. The framers of the Constitution were experienced legislators, capable of writing with great precision. In writing Article V, they rejected the exclusive language of Article XIII.
3. Article VII problems and resolution. Article VII of the Constitution provided for ratification by conventions of nine states. This plainly violated Article XIII of the Articles of Confederation (above) as well as the exclusive amendment procedures of several state constitutions. Madison resolved the contradictions of Article VII as follows: “The people were, in fact, the fountain of all power, and by resorting to them, all difficulties were got over. They could alter constitutions as they pleased.” James Wilson echoed, “…the people may change the constitutions whenever and however they please. This is a right of which no positive institution can ever deprive them.” More importantly, the people endorsed this view in the act of ratification.
4. The Preamble. The Preamble (We the People of the United States…do ordain and establish this Constitution) has an obvious, complementary meaning: that we have the power to alter or abolish it as well.
5. Ninth Amendment. According to one scholar, only three groups of rights are repeatedly called natural or unalienable in the Revolutionary declarations and state ratifying conventions: the individual right to “worship God according to the dictates of conscience”; the individual right of “defending life and liberty, acquiring, possessing and protecting property, and pursuing and obtaining happiness and safety”; and the right of a majority of the people to “alter and abolish” their government. This core of rights is, at a minimum, what rights…retained by the people in the Ninth Amendment means.
6. The future. If this proposal or something similar is ever ratified, then we will have proved the point again.

Akhil Reed Amar developed the case for Article V non-exclusivity here and here. For the Ninth Amendment, see Jeff Rosen here (registration required, see page 1082-3).

Of course, this is not currently the conventional wisdom, but the conventional wisdom can change.