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 techniques. 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 85μΩcm), are promising for spintronic devices exploiting the SHE.