The paper investigates the properties of Scalar-Induced Gravitational Waves (SIGWs), which are a class of primordial gravitational waves generated by second-order metric perturbations. The authors analyze the statistical properties of these waves, focusing on the impact of local non-Gaussianity in the primordial curvature perturbations on the GW spectrum. They derive the GW energy density ΩGW(f) up to fifth-order in the scalar seeds, considering all relevant non-Gaussian contributions without assuming any hierarchy among the non-Gaussian parameters. The study uses Wick's theorem and numerical high-dimensional integrations via Monte Carlo methods. The results are compared with the sensitivity of the LISA detector, which is expected to measure the amplitude, width, and peak of the GW spectrum with an accuracy of O(10^-4) and non-Gaussianity up to O(10^-3). The implications of these findings for the abundance of Primordial Black Holes (PBHs) are also discussed.The paper investigates the properties of Scalar-Induced Gravitational Waves (SIGWs), which are a class of primordial gravitational waves generated by second-order metric perturbations. The authors analyze the statistical properties of these waves, focusing on the impact of local non-Gaussianity in the primordial curvature perturbations on the GW spectrum. They derive the GW energy density ΩGW(f) up to fifth-order in the scalar seeds, considering all relevant non-Gaussian contributions without assuming any hierarchy among the non-Gaussian parameters. The study uses Wick's theorem and numerical high-dimensional integrations via Monte Carlo methods. The results are compared with the sensitivity of the LISA detector, which is expected to measure the amplitude, width, and peak of the GW spectrum with an accuracy of O(10^-4) and non-Gaussianity up to O(10^-3). The implications of these findings for the abundance of Primordial Black Holes (PBHs) are also discussed.