We present the first spatially resolved measurements of galaxy properties in the \textit{JWST} ERO SMACS0723 field. We perform a comprehensive analysis of five $5<z<9$ galaxies with spectroscopic redshifts from NIRSpec observations. We perform spatially resolved SED fitting with \textsc{Bagpipes}, using 6 NIRCam imaging bands spanning the wavelength range $0.8-5\mu$m. This approach allows us to study the internal structure and assembly of the first generations of galaxies. We find clear gradients both in the empirical colour maps, as well as in most of the estimated physical parameters. We find regions of considerably different specific star formation rates across each galaxy, which points to very bursty star-formation happening on small scales, not galaxy-wide. The integrated light is dominated by these bursty regions, which exhibit strong line emission, with the equivalent width of [\ion{O}{3}]+H$\beta$ reaching up to $\sim3000-4000$~Å rest-frame. Studying these galaxies in an integrated approach yields extremely young inferred ages of the stellar population ($<$10 Myr), which outshine older stellar populations that are only distinguishable in the spatially resolved maps. This leads to inferring $\sim0.5-1$ dex lower stellar masses by using single-aperture photometry, when compared to resolved analyses. Such systematics would have strong implications in the shape and evolution of the stellar mass function at these early times, particularly while samples are limited to small numbers of the brightest candidates. Furthermore, the evolved stellar populations revealed in this study imply an extended process of early galaxy formation that could otherwise be hidden behind the light of the most recently formed stars.