In the present paper, the authors consider degree 5 hyperbolic polynomials (HPs) in one variable (i.e., real and with all roots real). The authors are interested in such HPs whose number of equalities between roots of the polynomial and its derivatives is greater or equal to 4. The authors give a new method, based on resultants and subresultants, to calculate the overdetermined strata for degree 5 hyperbolic polynomials.