The fifth-order Korteweg-de Vries equation (KdV5) is a nonlinear partial differential equation used to model dispersive phenomena such as plasma waves and capillary-gravity water waves. For certain parameter regimes, KdV5 exhibits multi-pulse traveling wave solutions. Linear stability of these multi-pulse solutions is determined by eigenvalues near the origin representing the interaction between the individual pulses. In the case of periodic boundary conditions, we are able to use Lin’s method to locate these small eigenvalues. We give analytical criteria for the stability of these periodic multi-pulse solutions and also present numerical results to support our analysis.