  In this fifth paper of the series, we use the parametrized, spherically
symmetric explosion method PUSH to investigate the impact of eight different
nuclear equations of state (EOS). We present and discuss the explosion
properties and the detailed nucleosynthesis yields, and predict the remnant
(neutron star or black hole) for all our simulations. For this, we perform two
sets of simulations. One, a complete study of non-rotating stars from 11 to 40
M$_{\odot}$ at three different metallicities using the SFHo EOS. And two, a
suite of simulations for four progenitors (16 M$_{\odot}$ at three
metallicities and 25 M$_{\odot}$ at solar metallicity) for eight different
nuclear EOS. We compare our predicted explosion energies and yields to observed
supernovae and to the metal-poor star HD~84937. We find EOS-dependent
differences in the explosion properties and the nucleosynthesis yields.
However, when comparing to observations, these differences are not large enough
to rule out any EOS considered in this work.
