  The SO(4,2) isometries of AdS_5 are realized non-linearly on its
horospherical coordinates (x^m,\rho). On the other hand, Penrose twistors have
long been known to linearly realize these symmetries on 4-dimensional Minkowski
space, the boundary of AdS_5, parametrized by x^m. Here we extend the twistor
construction and define a pair of twistors, allowing us to include a radial
coordinate in the construction. The linear action of SO(4,2) on the twistors
induces the correct isometries of AdS_5. We apply this new construction to the
study of the dynamics of a massive particle in AdS_5. We show that in terms of
the twistor variables the action takes a simple form of a 1-dimensional gauge
theory. Our result might open up the possibility to find a simple worldvolume
action also for the string propagating on AdS_5.
