Vega, Sirius, beta Leo, alpha Car and alpha Cen A belong to a sample of twenty stellar sources used for the calibration of the detectors of the Short-Wavelength Spectrometer on board the Infrared Space Observatory (ISO-SWS). While general problems with the calibration and with the theoretical modelling of these stars are reported in Decin et al. (2003), each of these stars is discussed individually in this paper. As demonstrated in Decin et al. (2003), it is not possible to deduce the effective temperature, the gravity and the chemical composition from the ISO-SWS spectra of these stars. But since ISO-SWS is absolutely calibrated, the angular diameter (theta(d)) of these stellar sources can be deduced from their ISO-SWS spectra, which consequently yields the stellar radius (R), the gravity-inferred mass (M-g) and the luminosity (L) for these stars. For Vega, we obtained theta(d) = 3.35 +/- 0.20 mas, R = 2.79 +/- 0.17 R., M-g = 2.54 +/- 1.21 M. and L = 61 +/- 9 L.; for Sirius theta(d) = 6.17 +/- 0.38 mas, R = 1.75 +/- 0.11 R., M-g = 2.22 +/- 1.06 M. and L = 29 +/- 6 L.; for beta Leo theta(d) = 1.47 +/- 0.09 mas, R = 1.75 +/- 0.11 R., M-g = 1.78 +/- 0.46 M. and L = 15 +/- 2 L.; for alpha Car theta(d) = 7.22 +/- 0.42 mas, R = 74.39 +/- 5.76 R., M-g = 12.80(-6).(+24.95)(35) M. and L = 14573 +/- 2268 L. and for alpha Cen A theta(d) = 8.80 +/- 0.51 mas, R = 1.27 +/- 0.08 R., M-g = 1.35 +/- 0.22 M. and L = 1.7 +/- 0.2 L.. These deduced parameters are confronted with other published values and the goodness-of-fit between observed ISO-SWS data and the corresponding synthetic spectrum is discussed.