The paper is devoted to investigation of the first mixed problem for nonlinear fifth order equation in domain bounded with respect to time variable and unbounded with respect to space variables. Described equation generalizes the equation of beam vibrations in medium with resistance, which is studied in elasticity theory, for a case of any finite number of space variables. The conditions of the existence and uniqueness of generalized solution have been obtained. The classes of the existence and uniqueness are the spaces of local integrable functions.