Band structures of the pressure-induced, heavy-fermion superconductor Ce2Ni3Ge5 and its non-superconducting, mixed-valence isostructural (Ibam) counterpart Ce2Ni3Si5 have been calculated employing the full-potential local-orbital code. Both the local density approximation (LDA) and LDA+U approaches were applied. These investigations were focused particularly on the topology of the Fermi surfaces (FSs) of the compounds. The results show that the FSs are quite similar in these systems and exist in four bands, containing three-dimensional holelike and electronlike sheets. However, the specific FS nesting properties has been revealed only in Ce2Ni3Ge5. They support a previously postulated presence of antiferromagnetic spin fluctuations (SF) in the heavy-fermion superconducting state of this germanide under pressure. Such SF can be responsible for the pressure-induced unconventional superconductivity in this system.