With the development of 5th generation (5G) mobile networks people of different ages will be exposed in the upper part of the microwave spectrum. From the perspective of non-ionizing radiation dosimetry, an accurate analysis of age-dependent electromagnetic power deposition and resulting heating is required. In this study, we evaluate the effect of age on exposure at 26 GHz and 60 GHz. A near-surface tissue model illuminated by a plane wave is used to asses the exposure considering both frequency-independent and frequency-dependent limits. The age-related variation of the skin thickness and tissue electromagnetic properties has been considered. Moreover, the blood flow decrease rate has been taken into account to assess the age-dependent heating. Our results demonstrate that the overall variations of the power density, specific absorption rate (SAR) and heating in the near-surface tissues are limited to about 10-15%. These variations are mainly due to the tissue permittivity and blood flow change with age. In contrast to the transmitted power density that increases with age, the peak SAR decreases at both frequencies. The peak steady-state heating increases from 5 to 70 years old by roughly 11% at 26 GHz and 13% at 60 GHz.