The interaction between two neighboring third-order solitons was numerically studied under quintic nonlinear effect. The results show that the positive quintic nonlinear effect can lead to the shape of third-order soliton pair further worsening, in-phase and out-phase third-order soliton pair are both split under negative quintic nonlinear quickly. If the third-order soliton pair has the same phase, the two split optical pulses with lower peak value lie inside. It is found that the third-solitons attract each other and collide into one optical pulse. If the third-order soliton pair has the opposite phase, the two split optical pulses with lower peak value lie outside and keep the state of repulsion. When the third-soliton pair has opposite phase, the bigger the absolute value of negative quintic nonlinear parameter is, the more the number of solitons split from third-order soliton pair are. The results also show that the interactions between two neighboring third-order solitons may be well suppressed under appropriate parameters of the negative quintic nonlinearity.