  In this note, we generalize Gromov's reduction \cite{Gro20} from the
aspherical conjecture to the generalized filling radius conjecture to the
smooth $\mathbb Q$-homology vanishing conjecture for hypersurface. In
particular, we can show that any continuous map from a closed $4$-manifold
admitting positive scalar curvature to an aspherical $5$-manifold induces zero
map in $H_4(\cdot,\mathbb Q)$. As a corollary, we obtain the following
splitting theorem: if a complete aspherical $5$-manifold has nonnegative scalar
curvature and two ends, then it splits into the Riemannian product of a closed
flat manifold and the real line.
