It is established that the multiferroics RMn(2)O(5) crystallize in the centrosymmetric Pbam space group and that the magnetically induced electric polarization appearing at low temperature is accompanied by a symmetry breaking. However, both our present x-ray study-performed on compounds with R=Pr,Nd,Gd,Tb, and Dy-and first-principles calculations unambiguously rule out this picture. Based on structural refinements, geometry optimization, and physical arguments, we demonstrate in this Letter that the actual space group is likely to be Pm. This turns out to be of crucial importance for RMn(2)O(5) multiferroics since Pm is not centrosymmetric. Ferroelectricity is thus already present at room temperature, and its enhancement at low temperature is a spin-enhanced process. This result is also supported by direct observation of optical second harmonic generation. This fundamental result calls into question the actual theoretical approaches that describe the magnetoelectric coupling in this multiferroic family.