The formation of an electron hole on an AlO(4)H center of the H-ZSM-5 zeolite has been studied by a hybrid quantum mechanics/shell-model ion-pair potential approach. The Becke-3-Lee-Yang-Parr (B3LYP) and Becke-Half&Half-Lee-Yang-Parr (BHLYP) hybrid density functionals yield electron holes of different nature, a delocalized hole for B3LYP and a hole localized on one oxygen atom for BHLYP. Comparison with coupled cluster calculations including single and double substitutions and with perturbative treatment of triple substitutions CCSD(T) and with experimental data for similar systems indicate that the localized description obtained with BHLYP is more accurate. Generation of the electron hole produces a substantial geometry relaxation, in particular an elongation of the Al-O distance to the oxygen atom with the unpaired electron. The zeolite framework stabilizes the positive charge by long-range effects. Our best estimates for the vertical and adiabatic ionization energies are 9.6-10.1 and 8.4-8.9 eV, respectively. Calculations for silicalite, the all-silica form of ZSM-5, also yield a localized electron hole, but the energy cost of the process is larger by 0.6-0.7 eV. The deprotonation energy of H-ZSM-5 is found to decrease from 12.86 to 11.40 eV upon electron hole formation.