We present the results from the Suzaku X-ray observations of five flat-spectrum radio quasars (FSRQs), namely PKS0208-512, Q0827+243, PKS1127-145, PKS1510-089 and 3C 454.3. All these sources were additionally monitored simultaneously or quasi-simultaneously by the Fermi satellite in gamma-rays and the Swift UVOT in the UV and optical bands, respectively. We constructed their broad-band spectra covering the frequency range from 10^14 Hz up to 10^25 Hz, and those reveal the nature of high-energy emission of luminous blazars in their low-activity states. The analyzed X-ray spectra are well fitted by a power-law model with photoelectric absorption. In the case of PKS0208-512, PKS1127-145, and 3C 454.3, the X-ray continuum showed indication of hard-ening at low-energies. Moreover, when compared with the previous X-ray observations, we see a significantly increasing contribution of low-energy photons to the total X-ray fluxes when the sources are getting fainter. The same behavior can be noted in the Suzaku data alone. A likely explanation involves a variable, flat-spectrum component produced via inverse-Compton (IC) emission, plus an additional, possibly steady soft X-ray component prominent when the source gets fainter. This soft X-ray excess is represented either by a steep powerlaw (photon indices Gamma ~ 3 - 5) or a blackbody-type emission with temperatures kT ~ 0.1-0.2 keV. We model the broad-band spectra spectra of the five observed FSRQs using synchrotron self-Compton (SSC) and/or external-Compton radiation (ECR) models. Our modeling suggests that the difference between the low and high-activity states in luminous blazars is due to the different total kinetic power of the jet, most likely related to varying bulk Lorentz factor of the outflow within the blazar emission zone.Read less <