PuCoGa$_5$ has emerged as a prototypical heavy-fermion superconductor, with its transition temperature ($T_csimeq18.5$ K) being the highest amongst such materials. Nonetheless, a clear description as to what drives the superconducting pairing is still lacking, rendered complicated by the notoriously intricate nature of plutoniums 5$f$ valence electrons. Here, we present a detailed $^{69,71}$Ga nuclear quadrupole resonance (NQR) study of PuCoGa$_5$, concentrating on the systems normal state properties near to $T_c$ and aiming to detect distinct signatures of possible pairing mechanisms. In particular, the quadrupole frequency and spin-lattice relaxation rate were measured for the two crystallographically inequivalent Ga sites and for both Ga isotopes, in the temperature range 1.6 K - 300 K. No evidence of significant charge fluctuations is found from the NQR observables. On the contrary, the low-energy dynamics is dominated by anisotropic spin fluctuations with strong, nearly critical, in-plane character, which are effectively identical to the case of the sister compound PuCoIn$_5$. These findings are discussed within the context of different theoretical proposals for the unconventional pairing mechanism in heavy-fermion superconductors.
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