In this work, the analysis and generalization of data on the elemental, phase and surface composition, crystal structure and microstructure of MFI-type HZSM-5 with Si/Al = 12, 25, 40, 300 were presented. Relationships between HZSM-5 silicate modulus (Si/Al) and pore volume, specific surface, the area of framework voids were established. Data obtained by electron microscopy and energy dispersive X-ray microanalysis explained the discrepancy between HZSM-5 real composition and the initial one. Samples with the maximum content of Brønsted (HZSM-5 with Si/Al = 25) and Lewis (HZSM-5 with Si/Al = 12) acid sites responsible for the catalytic activity were identified using diffuse reflectance Fourier transform infrared spectroscopy. N2O decomposition reaction rate was found to decrease in the row HZSM-5(25) > HZSM-5(12) > HZSM-5(40) > HZSM-5(40)С>>HZSM-5(300). The high N2O decomposition rate demonstrated by HZSM-5(25) makes it promising catalyst. The second phase of iron oxides and the presence of faceted particles {001} oriented in HZSM-5(25) were shown to contribute to its maximum catalytic activity in N2O decomposition. The applied methodology for studying aluminosilicalites with different silicate modules and the revealed correlations can provide a fundamental perspective in studying other zeolites or modifying data.