  In this paper we settle a special case of the Grassmann convexity conjecture
formulated earlier by B.and M.Shapiro. We present a conjectural formula for the
maximal total number of real zeros of the consecutive Wronskians of an
arbitrary fundamental solution to a disconjugate linear ordinary differential
equation with real time. We show that this formula gives the lower bound for
the required total number of real zeros for equations of an arbitrary order
and, using our results on the Grassmann convexity, we prove that the
aforementioned formula is correct for equations of orders $4$ and $5$.
