Experimental and theoretical cross sections are reported for single-photon single ionization of W\(^{5+}\) ions. Absolute measurements were conducted employing the photon-ion merged-beams technique. Detailed photon-energy scans were performed at (67\(\pm\)10)~meV resolution in the 20 -- 160 eV range. In contrast to photoionization of tungsten ions in lower charge states, the cross section is dominated by narrow, densely-spaced resonances. Theoretical results were obtained from a Dirac-Coulomb R-matrix approach employing a basis set of 457 levels providing cross sections for photoionization of W\(^{5+}\) ions in the \(4f^{14}5s^2 5p^6 5d \; {^2}{\rm D}_{3/2}\) ground level as well as the \(4f^{14}5s^2 5p^6 5d \; {^2}{\rm D}_{5/2}\) and \(4f^{14}5s^2 5p^6 6s \; {^2}{\rm S}_{1/2}\) metastable excited levels. Considering the complexity of the electronic structure of tungsten ions in low charge states, the agreement between theory and experiment is satisfactory.