A model-independent determination of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix (CKM) element Vus from five measured strangeness changing hyperon semileptonic decays is performed. Flavor SU(3) symmetry breaking effects in the leading vector and axial-vector form factors are analyzed in the framework of the 1/Nc expansion of QCD. A fit to experimental data allows one to extract the value Vus = 0.2199 ± 0.0026, which is comparable to the one from Ke3 decays. This reconciliation is achieved through second-order symmetry breaking effects of a few percent in the form factors f1, which increase their magnitudes over their SU(3) predictions.