The method of counting maxima of excitation curves in the region of the occurrence of nuclear cross section fluctuations is extended to the case of the more realistic maxima defined as a sequence of five points instead of the simpler and commonly used case of a sequence of three points of an excitation curve. The dependence of the coefficient b (5)( κ), relating the number of five-point maxima and the mean level width Γ of the compound nucleus, on the relative distance κ of excitation curve points is calculated. The influence of the random background on the coefficient b (5)( κ) is discussed and a comparison with the properties of the three-point coefficient b (3)( κ) is made — also in connection with the contribution of the random background. The calculated values of b (5)( κ) are well reproduced by the data obtained from the analysis of artificial excitation curves.