We investigate the cosmological implications of the recently constructed five-dimensional braneworld cosmology with gravitating Nambu-Goto matching conditions. Inserting both matter and radiation sectors, we extract analytical cosmological solutions. Additionally, we use observational data from Type Ia supernovae and baryon acoustic oscillations, along with requirements of big bang nucleosynthesis and cosmic microwave background radiation, in order to impose constraints on the parameters of the model. We find that the scenario at hand is in good agreement with observations, and thus a small departure from the standard Randall-Sundrum scenario is allowed. However, the concordance Lambda CDM cosmology is still favored comparing to both the standard braneworld model and the present scenario.