We solve exactly the equations of 5D general relativity for the case o
f a spinning test object moving in a circular orbit in a Schwarzschild
-like spacetime augmented by one extra dimension. All of the classical
tests give their standard results, but the spin axis precesses at a d
ifferent rate in 4D and 5D. This suggests that the dimensionality of t
he world could be tested using a gyroscope in Earth orbit.