Photometric data from the Transiting Exoplanet Survey Satellite (TESS) was analysed using the Bayesian fitting tool juliet to investigate two faint transiting exoplanet targets: the known planet TOI 4587 and the candidate TOI 5274. Models were fitted to all available TESS observations to determine orbital periods, transit geometries and limb-darkening parameters. The derived orbital periods were found to be broadly consistent with published values, although differences between values exceeded quoted uncertainties. TOI 4587 produced a well-constrained solution, while TOI 5274 exhibited broad posterior distributions. Both phase-folded light curves displayed characteristic U-shaped exoplanetary transit signatures. However, the fits performed poorly on the raw photometric data, likely due to the faintness of the targets.