High-harmonic generation from solid films is an attractive method for converting infrared laser pulses to ultraviolet and vacuum ultraviolet wavelengths and for examining the films using the generation process. In this work, AlN thin films grown on a sapphire substrate are studied. Below-band-gap third harmonics and above-band-gap fifth harmonics were generated using a Ti:sapphire oscillator running at 800 nm. A strong enhancement of the fifth-harmonic signal in the forward direction was observed from thicker 39 nm and 100 nm films compared to thinner 8 nm and 17 nm films. For the fifth harmonic generated in the backward direction, and also for the third harmonic in both the forward and backward directions, only a weak dependence of the harmonic signal on the film thickness was measured. Using both X-ray diffraction and dependence of the fifth harmonic on the laser polarization measurements, these behaviors are attributed to the crystallization and the grain size of the films, promising fifth-harmonic generation as a suitable tool to study AlN film properties.