  An 1861 theorem of Hermite asserts that for every field extension $E/F$ of
degree $5$ there exists an element of $E$ whose minimal polynomial over $F$ is
of the form $f(x) = x^5 + c_2 x^3 + c_4 x + c_5$ for some $c_2, c_4, c_5 \in
F$. We give a new proof of this theorem using techniques of Galois cohomology,
under a mild assumption on $F$.
