The dielectric response of pentagonal defects in multilayer graphene nano-cones has been studied by electron energy loss spectroscopy and ab initio simulations. At the cone apex, a strong modification of the dielectric response is observed below the energy of the π plasmon resonance. This is attributed to π → π* interband transitions induced by topology-specific resonant π bonding states as well as π*-σ* hybridization. It is concluded that pentagonal defects strongly affect the local electronic structure in such a way that multi-walled graphene nano-cones should show great promise as field emitters.