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We construct the integrals of motion for the 5D deformed Kepler system withnon-central potentials in $su(2)$ Yang-Coulomb monopole field. We show thatthese integrals form a higher rank quadratic algebra $Q(3; L^{so(4)},T^{su(2)})\oplus so(4)$, with structure constants involving the Casimiroperators of $so(4)$ and $su(2)$ Lie algebras. We realize the quadratic algebrain terms of the deformed oscillator and construct its finite-dimensionalunitary representations. This enable us to derive the energy spectrum of thesystem algebraically. Furthermore we show that the model is multiseparable andallows separation of variables in the hyperspherical and parabolic coordinates.We also show the separability of its 8D dual system (i.e. the 8D singularharmonic oscillator) in the Euler and cylindrical coordinates.

Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang-Coulomb monopole interaction