Low-energy (<20 eV) electrons (LEEs) can resonantly interact with DNA to form transient anions (TAs) of fundamental units, inducing single-strand breaks (SSBs), and cluster damage, such as double-strand breaks (DSBs). Shape resonances, which arise from electron capture in a previously unfilled orbital, can induce only a SSB, whereas a single core-excited resonance (i.e., two electrons in excited orbitals of the field of a hole) has been shown experimentally to cause cluster lesions. Herein, we show from time-dependent density functional theory (TDDFT) that a core-excited resonance can produce a DSB, i.e., a single 5 eV electron can induce two close lesions in DNA. We considered the nucleotide with the G−C base pair (ds[5′-G-3′]) as a model for electron localization in the DNA double helix and calculated the potential energy surfaces (PESs) of excited states of the groundstate TA of ds[5′-G-3′], which correspond to shape and core-excited resonances. The calculations show that shape TAs start at ca. 1 eV, while core-excited TAs occur only above 4 eV. The energy profile of each excited state and the corresponding PES are obtained by simultaneously stretching both C5′−O5′ bonds of ds[5′-G-3′]. From the nature of the PES, we find two dissociative (σ*) states localized on the PO 4 groups at the C5′ sites of ds[5′-G-3′]. The first σ* state at 1 eV is due to a shape resonance, while the second σ* state is induced by a core-excited resonance at 5.4 eV. As the bond of the latter state stretches and arrives close to the dissociation limit, the added electron on C transfers to C5′ phosphate, thus demonstrating the possibility of producing a DSB with only one electron of ca. 5 eV.