  We prove that proper biharmonic hypersurfaces with constant scalar curvature
in Euclidean sphere $\mathbb S^5$ must have constant mean curvature. Moreover,
we also show that there exist no proper biharmonic hypersurfaces with constant
scalar curvature in Euclidean space $\mathbb E^5$ or hyperbolic space $\mathbb
H^5$, which give affirmative partial answers to Chen's conjecture and
Generalized Chen's conjecture.
