Abstract: We present an efficient approach to studying the spectra and eigenstates for the model describing interactions among five bosonic modes without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter $\lambda $ for a class of models describing five-mode multiphoton process. The parameter is determined by the roots of a polynomial and is solvable analytically or numerically.

Key words: spectrum, eigenstate, five-mode multiphonton process