The x-ray transitions in Cu- and Ni-like tungsten ions in the 5.19-5.26 angstrom wavelength range that are relevant as a high-temperature tokamak diagnostic, in particular for JET in the ITER-like wall configuration, have been studied. Tungsten spectra were measured at the upgraded Shanghai-Electron Beam Ion Trap operated with electron-beam energies from 3.16 to 4.55 keV. High-resolution measurements were performed by means of a flat Si 111 crystal spectrometer equipped by a CCD camera. The experimental wavelengths were determined with an accuracy of 0.3-0.4 m angstrom. The wavelength of the ground-state transition in Cu-like tungsten from the 3p(5)3d(10)4s4d [(3/2,(1/2,5/2)(2)](1/2) level was measured. All measured wavelengths were compared with those measured from JET ITER-like wall plasmas and with other experiments and various theoretical predictions including COWAN, RELAC, multiconfigurational Dirac-Fock (MCDF), and FAC calculations. To obtain a higher accuracy from theoretical predictions, the MCDF calculations were extended by taking into account correlation effects (configuration-interaction approach). It was found that such an extension brings the calculations closer to the experimental values in comparison with other calculations.