  The 5D Kepler system possesses many interesting properties. This system is
superintegrable and also with a $su(2)$ nonAbelian monopole interaction
(Yang-Coulomb monopole). This system is also related to a 8D isotropic harmonic
oscillator by a Hurwitz transformation. We introduce a new superintegrable
Hamiltonian that consists in a 5D Kepler system with new terms of
Smorodinsky-Winternitz type. We obtain the integrals of motion of this systems.
They generate a quadratic algebra with structure constants involving the
Casimir operator of a $so(4)$ Lie algebra. We also show that this system
remains superintegrable with a $su(2)$ nonAbelian monopole (generalized
Yang-Coulomb monopole). We study this system using parabolic coordinates and
obtain from Hurwitz transformation its dual that is a 8D singular oscillator.
This 8D singular oscillator is also a new superintegrable system and
multiseparable. We obtained its quadratic algebra that involves two Casimir
operators of $so(4)$ Lie algebras. This correspondence is used to obtain
algebraically the energy spectrum of the generalized Yang Coulomb monopole.
