In this paper we generated a new procedure called interval midpoint zoro symmetric single-step IMZSS2-5D procedure which is an extension from the existing ISS2 procedure. This procedure needs some pre-conditions for the initial interval to converge to the zeros respectively, starting with some disjoint intervals, each of which contains a polynomial zero. The IMZSS2-5D will produce a set of intervals of smallest possible width such that each interval includes one or more zeros of the polynomial from a given initial interval. The efficiency of the procedure is measured based on the CPU times, number of iterations and the value of the intervals width after satisfying the convergence criterion. Six test polynomials are used to verify the procedure. The numerical results are obtained by using MATLAB. The results indicated that the IMZSS2-5D procedure outperformed the existing ISS2 procedure. Hence, it is efficient to use IMZSS2-5D procedure for simultaneously bounding the polynomial zeros. © 2018 Author(s).