The classical tests of general relativity-light deflection, time delay and perihelion shift-are applied,along with the geodetic precession test,to the five-dimensional extension of the theory known as Kaluza-Klein gravity,using an analogue of the four-dimensional Schwarzschild metric.The perihelion advance and geodetic precession calculations are generalized for the first time to situations in which the components of momentum and spin along the extra coordinate do not vanish. Existing data on light-bending around the Sun using long-baseline radio interferometry,ranging to Mars using the Viking lander,and the perihelion precession of Mercury all constrain a small parameter b associated with the extra part of the metric to be less than |b| < 0.07 in the solar system.An order-of-magnitude increase in sensitivity is possible from perihelion precession,if better limits on solar oblateness become available.Measurement of geodetic precession by the Gravity Probe B satellite will improve this significantly,probing values of b with an accuracy of one part in 104 or more.