We present measurements of the Spin Hall Effect (SHE) in AuW and AuTa alloys for a large range of W or Ta concentrations by combining experiments on lateral spin valves and Ferromagnetic-Resonance/spin pumping technique. The main result is the identification of a large enhancement of the Spin Hall Angle (SHA) by the side-jump mechanism on Ta impurities, with a SHA as high as + 0.5 (i.e $50%$) for about 10% of Ta. In contrast the SHA in AuW does not exceed + 0.15 and can be explained by intrinsic SHE of the alloy without significant extrinsic contribution from skew or side-jump scattering by W impurities. The AuTa alloys, as they combine a very large SHA with a moderate resistivity (smaller than $85,muOmega.cm$), are promising for spintronic devices exploiting the SHE.