The recent hypothesis of a possible new fifth quark flavour, beauty (or bottom), following from the discovery of the gamma resonances, is considered here in the context of the Weinberg spectral-function sum rules. The authors find as a consequence new equal-spacing mass relations and general mass constraints for the vector mesons with the new flavour. In a restricted symmetry domain they predict the masses of some of these mesons and discuss the results in so far as they shed light on the breaking of SU(5) symmetry and the approximations involved in the Weinberg sum rules.