A century on from its discovery, a complete fundamental understanding of superconductivity is still missing. Considerable research efforts are currently devoted to elucidating mechanisms by which pairs of electrons can bind together through the mediation of a boson field different than the one associated to the vibrations of a crystal lattice. PuCoGa_5, a 5f-electron heavy-fermion superconductor with a record critical temperature T_c=18.5 K, is one of the many compounds for which the short-range, isotropic attraction provided by simple electron-phonon coupling does not appear as an adequate glue for electron pairing. Here, we report the results of point-contact spectroscopy measurements in single crystals of PuCoGa_5. Andreev reflection structures are clearly observed in the low-temperature spectra, and unambiguously prove that the paired superconducting electrons have wavefunction with the d-wave symmetry of a four-leaf clover. A straightforward analysis of the spectra provide the amplitude of the gap and its temperature dependence, Delta(T). We obtain Delta(T -> 0) = 5.1 pm 0.3 meV and a gap ratio, 2Delta/k_B T_c = 6.5 pm 0.3, indicating that the compound is in the regime of strong electron-boson coupling. The gap value and its temperature dependence can be well reproduced within the Eliashberg theory for superconductivity if the spectral function of the mediating bosons has a spin-fluctuations-like shape, with a peak energy of 6.5 meV. Electronic structure calculations, combining the local density approximation with an exact diagonalization of the Anderson impurity model, provide a hint about the possible origin of the fluctuations.