The SO(4,2) isometries of AdS(5) are realized non-linearly on its horospherical coordinates (x(m), rho). On the other hand, Penrose twisters 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 twister construction and define a pair of twisters, allowing us to include a radial coordinate in the construction. The linear action of SO(4,2) on the twisters 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 twister variables the action takes a simple form of a 1-dimensional gauge theory. Our result might open up the possibility to find a simple world volume action also for the string propagating on AdS(5).