We present photometric observations of the transiting exoplanets HAT-P-53b and XO-5b by the Rozhen 2 m telescope. The modeling of the HAT-P-53b transit required bigger planet radius than the previously published value due to the bigger depth of the newly-observed transit. The transit solution of XO-5b led to values of the fitted parameters within the errors of the previously published results. Based on time span of around 9 years we improved the orbital period of XO-5b to a value of 4.187751515 d. The quality of our data does not allow determination of the planet temperatures by the transit solutions. Our results confirmed the Jupiter type of the two targets. The more bloated nature of HAT-P-53b is a result of its considerable closer orbit and higher temperature of the host star. The best fits of the newly-observed transits of HAT-P-53b and XO-5b correspond to quadratic limb-darkening law of their host stars whose coefficients were determined. The high sensitivity of the transit solutions to the stellar limb-darkening law and its coefficient(s) is proposed as a tool for precise empirical investigation of the limb-darkening effect of host stars and its interpretation.