In this paper, for any rational prime p and for a fixed positive integer i_p, we provide infinite families of number fields defined by irreducible quintinomials of type xⁿ+ax^m+bx²+cx+d in Z[x] satisfying ν_p(i(K))=i_p. We illustrate our results by some computational examples.

The author is deeply grateful to the anonymous referee for their valuable comments and suggestions, which have tremendously improved the quality of this paper, as well as for their prompt and efficient review. Also, he extends his sincere thanks to Professor Lhoussain El Fadil for his help and encouragement.