Symmetries, Spinning Particles and the TCFH of D=4,5 Minimal Supergravities

We find that spinning particles with suitable couplings propagating in certain supersymmetric backgrounds of $D=4$, $N=2$ and $D=5$, $N=1$ minimal supergravities are invariant under symmetries generated by the twisted covariant form hierarchies of these theories. We also compare our results with the symmetries of spinning particles generated by Killing-Yano forms which are responsible for the separability properties of some gravitational backgrounds.