  In this work, which is based on spin-2 vectors and traceless spin-2 tensors,
an effective Hamiltonian is constructed with a linearly dispersive five-fold
degenerate point with spin-2 vector-momentum couplings. For the model without
spin-2 vector-tensor coupling, the topological Chern numbers of five bands are
calculated as 4, 2, 0, -2, -4. After including spin-2 vector-tensor coupling,
separate topological Chern numbers are obtained for different couplings. A
cubic lattice of atoms with five internal states is designed to realize two
five-fold degenerate points. The Chern numbers of the bands can be changed by
tuning the coupling coefficient. In this work we propose a theoretical design
to obtain spin-2 quasi-particles.
