The cubic-quintic complex Ginzburg-Landau equation (CQCGLE) is a master equation that has been used to describe passively mode-locked fiber lasers. The main characteristics of very high amplitude (VHA) soliton solutions of the CQCGLE are described numerically and using the method of moments, both in the normal and anomalous dispersion regimes of the fiber laser. The region of existence of such pulses is found numerically in the plane defined by the dispersion and the nonlinear gain saturation parameters. High-energy ultrashort pulses are found mainly in the normal dispersion region, which agrees with the experimental observations reported by other authors. The impact of the higher-order reactive nonlinearity on VHA solitons is also described, focusing mainly in the normal dispersion regime. In the presence of this effect, the amplitude and the energy of the VHA pulses decrease, whereas pulse formation is observed for much higher absolute values of dispersion. The region of existence of the VHA pulses under this effect is found in the semiplane defined by the dispersion and the nonlinear gain.