  While the 10d type IIB supergravity action evaluated on AdS$_5\times S^5$
solution vanishes, the 5d effective action reconstructed from the equations of
motion using $M^5 \times S^5$ compactification ansatz is proportional to the
AdS$_5$ volume. The latter is consistent with the conformal anomaly
interpretation in AdS/CFT context. We show that this paradox can be resolved
if, in the case of $M^5 \times X^5$ topology, the 10d action contains an
additional 5-form dependent "topological" term $\int F_{5M} \wedge F_{5X}$. The
presence of this term is suggested also by gauge-invariance considerations in
the PST formulation of type IIB supergravity action. We show that this term
contributes to the 10d action evaluated on the D3-brane solution.
