Pentamer cluster of azodicarbonamide (ADA) based on the crystalline structure was investigated for the equilibrium structure, the stabilization energies, and the vibrational properties at various levels of the density functional theory. Stretching force constants of N${cdot}{cdot}{cdot}$H or O${cdot}{cdot}{cdot}$H, and angle-bending force constants of N-H${cdot}{cdot}{cdot}$N or N-H${cdot}{cdot}{cdot}$O for intermolecular hydrogen bonds in the pentamer cluster were obtained in 0.2-0.5 mdyn/$AA$ and 1.6-2.0 mdyn$AA$, respectively. The geometry of central ADA molecule fully hydrogen bonded with other four molecules shows good coincidence to the crystalline structure except the bond distances of N-H. Calculated Raman and infrared spectra of central ADA molecule in cluster represent well the experimental spectra of ADA obtained in the solid state compared to a single molecule. Detailed structural and vibrational properties of central ADA molecule in the pentamer cluster are presented.