On common index divisors and monogenity of certain number fields defined by x^5+ax+b

Let K = Q(α) be a number field, where α satisfies the monic irreducible polynomial F (x) = x5 + ax + b belonging to Zx. The purpose of this paper is to caracterise when a prime p is a common index divisor of K. More precisely, we give explicitly a necessary and sufficient conditions, on a and b for which K is not monogenic. Some useful examples are also given.