  Recently a new $\Delta$ method for deducing the energy and asymptotic
normalization coefficient (ANC) from phase-shift data has been formulated and
applied to resonance states. This differs from the conventional effective-range
function (ERF) method by fitting only the nuclear part of the ERF. It also
differs from the method which was proposed for bound states by Ram\'irez
Su\'arez and Sparenberg (see Ref. below) which also named the $\Delta$ method
where a pole condition defines by the Eq. $\Delta_l=0$ ($\Delta_l$ is the
function in the ERF determined only by the scattering phase shift). Here the
standard pole condition, including the Coulomb part into the relate equation,
is used for a resonant state. It has been shown that the ERF method does not
work for large-charge colliding nuclei. Moreover, even for lower charges it is
not clear that the results of the ERF method are accurately enough. The Coulomb
part forms a background, which smooths an ERF energy dependence. Therefore, one
needs to find when the ERF method becomes inaccurate and this requires
recalculating some published results by the $\Delta$ method. This project has
already been started in a recent paper for resonances in the $\alpha$-$\alpha$
scattering. Here this method is applied using the $\Delta_l$-function fittings
to the experimental $p$-${}^4$He scattering phase-shift data in the $P_{3/2}$
and $P_{1/2}$ resonance states. The calculation results are compared with those
obtained earlier by the ERF method. The main changes concern resonance energy
and width.
