  As an extension of previous works on classical tests of Kaluza-Klein (KK)
gravity and as an attempt to find more stringent constraints on this theory,
its effects on physical experiments and astronomical observations conducted in
the Solar System are studied. We investigate the gravitational time delay at
inferior conjunction caused by KK gravity, and use new Solar System ephemerides
and the observation of \textit{Cassini} to strengthen constraints on KK gravity
by up to two orders of magnitude. These improved upper bounds mean that the
fifth-dimensional space in the soliton case is a very flat extra dimension in
the Solar System, even in the vicinity of the Sun.
