Within an extended chiral constituent quark formalism, we investigate contributions from all possible five-quark components in the octet baryons to the pion-baryon (${\ensuremath{\sigma}}_{\ensuremath{\pi}B}$) and strangeness-baryon (${\ensuremath{\sigma}}_{sB}$) sigma terms: $B\ensuremath{\equiv}N,\mathrm{\ensuremath{\Lambda}},\mathrm{\ensuremath{\Sigma}},\mathrm{\ensuremath{\Xi}}$. The probabilities of the quark-antiquark components in the ground-state baryon octet wave functions are calculated by taking the baryons to be admixtures of three- and five-quark components, with the relevant transitions handled via the $^{3}{\mathrm{P}}_{0}$ mechanism. Predictions for ${\ensuremath{\sigma}}_{\ensuremath{\pi}B}$ and ${\ensuremath{\sigma}}_{sB}$ obtained by using input parameters taken from the literature are reported. Our results turn out to be, in general, consistent with the findings via lattice QCD and chiral perturbation theory.