We present a spatially resolved analysis of four star-forming galaxies at z = 4.44-5.64 using data from the JWST Public Release Imaging for Extragalactic Research (PRIMER) and ALMA-[C II] Resolved ISm in STar-forming galaxies with ALma (CRISTAL) surveys to probe the stellar and interstellar medium properties on the sub-kpc scale. In the 1-5 mu m JWST NIRCam imaging we find that the galaxies are composed of multiple clumps (between 2 and similar to 8) separated by similar or equal to 5kpc, with comparable morphologies and sizes in the rest-frame ultraviolet (UV) and optical. Using BAGPIPES to perform pixel-by-pixel spectral energy distribution (SED) fitting to the JWST data, we show that the star formation rate (SFR) (similar or equal to 25M(circle dot)yr(-1)) and stellar mass (log10(M star/M-circle dot) similar or equal to 9.5) derived from the resolved analysis are in close (less than or similar to 0.3dex) agreement with those obtained by fitting the integrated photometry. In contrast to studies of lower mass sources, we thus find a reduced impact of outshining of the older (more massive) stellar populations in these normal z similar or equal to 5 galaxies. Our JWST analysis recovers bluer rest-frame UV slopes (beta similar or equal to -2.1) and younger ages (similar or equal to 100Myr) than archival values. We find that the dust continuum from ALMA-CRISTAL seen in two of these galaxies correlates, as expected, with regions of redder rest-frame UV slopes and the SED-derived AV, as well as the peak in the stellar mass map. We compute the resolved IRX-beta relation, showing that the IRX is consistent with the local starburst attenuation curve and further demonstrating the presence of an inhomogeneous dust distribution within the galaxies. A comparison of the CRISTAL sources to those from the FirstLight zoom-in simulation of galaxies with the same M star and SFR reveals similar age and colour gradients, suggesting that major mergers may be important in the formation of clumpy galaxies at this epoch.