mixing orbitals to result in hybrids not only offers new opportunities for electrons to store, but also determines what shape this hybrid has to have: the rule of "conservation of symmetry" requires that the sum total of symmetries of parent orbitals equals the sum total of symmetries of resulting orbitals .
now, if you wish to construct the 5 hybrid orbitals of a trigonal-bipyramidal structure by using 1 * s , 3 * p and 1 * "?" , using another s ( i.e. another spherical symmetry) for "?" would lead you exactly nowhere: you need someting "with a direction" ( like, for example, a d-orbital) instead
that's why s is of no use , and hence isn't used for PCl5 , even though 4s in the pure atom of phosphorus, in the oxidation state of zero , in vacuum, might look more inviting at a first glance.
regards
Ingo