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 ∈ F . We give a new proof of this theorem using techniques of Galois cohomology, under a mild assumption on F .2010 Mathematics Subject Classification. 12G05, 14G05.