The onset of a Griffiths-like phase has been observed in Tb5Si2Ge2 (TC=110 K) by means of magnetic susceptibility and small-angle neutron scattering experiments. We show the growth of a ferromagnetic cluster system characterized by an inverse susceptibility exponent lower than unity at TC<T<TG approximately 200 K. We suggest that the Griffiths-like state is originated by local disorder within the crystallographic structure, stabilized and enhanced by competing intralayer and interlayer magnetic interactions. Both factors thus promote segregation of nanometric regions with ferromagnetic interactions.