The Discriminant of a Dihedral Quintic Field Defined by a Trinomial $X^5 + aX + b$ Let $X^5 + aX + b \in Z[X]$ have Galois group $D_5$. Let $\theta$ be a root of $X^5 + aX + b$. An explicit formula is given for the discriminant of $Q(\theta)$. Keywords:dihedral quintic field, trinomial, discriminantCategories:11R21, 11R29