  The study of the uniqueness and nondegeneracy of ground state solutions to
semilinear elliptic equations is of great importance because of the resulting
energy landscape and its implications for the various dynamics. In [AIKN3],
semilinear elliptic equations with combined power-type nonlinearities involving
the Sobolev critical exponent are studied. There, it is shown that if the
dimension is four or higher, and the frequency is sufficiently small, then the
positive radial ground state is unique and nondegenerate. In this paper, we
extend these results to the case of high frequencies when the dimension is five
and higher. After suitably rescaling the equation, we demonstrate that the main
behavior of the solutions is given by the Sobolev critical part for which the
ground states are explicit, and their degeneracy is well characterized. Our
result is a key step towards the study of the different dynamics of solutions
of the corresponding nonlinear Schr\"odinger and Klein-Gordon equations with
energies above the energy of the ground state. Our restriction on the dimension
is mainly due to the existence of resonances in dimension three and four.
