We study the nonlinear excitations in the integrable fifth-order nonlinear Schr(o)dinger equation on a continuous wave background.The excited condition of each localized wave is demonstrated via concise phase diagrams.In particular,the rule of transition between asymmetric and symmetric multi-peak solitons is revealed.It is shown that the initial phase modulation can induce the transition and the transition condition is demonstrated exactly.Interestingly,our result shows that although the multi-peak solitons exhibit structural diversity,both the asymmetric and symmetric states possess an identical asymmetric spectrum structure.