Common index divisor of the number fields defined by

Let K=Q(θ ) be an algebraic number field with θ a root of an irreducible polynomial x⁵+ax+b∈ Z[x] . In this paper, for every rational prime p , we provide necessary and sufficient conditions on $a,\,~b$ so that p is a common index divisor of K . In particular, we give sufficient conditions on $a,\,~b$ for which K is non-monogenic. We illustrate our results through examples.