Abstract: By using the stochastic averaging method based on the generalized harmonic function, this paper established the Pontryagin equation and backward Kolmogorov equation of 5DOF strongly nonlinear vibration system under Gaussian white noises excitations. The mean first-passage time and conditional reliability function and the conditional probability density function of the mean first-passage time were obtained from solving the above two high-dimensional partial differential equations. All theoretical results are verified by Monte Carlo digital simulation.