The potential health risks of exposure to radiofrequency electromagnetic fields from mobile communications technologies have raised societal concerns. Guidelines have been set to protect the population (e.g. non-specific heating above 1°C under exposure to radiofrequency fields), but questions remain regarding the potential biological effects of non-thermal exposures. With the advent of the fifth generation (5G) of mobile communication, assessing whether exposure to this new signal induces a cellular stress response is one of the mandatory steps on the roadmap for a safe deployment and health risk evaluation. Using the BRET (Bioluminescence Resonance Energy-Transfer) technique, we assessed whether continuous or intermittent (5 min ON/10 min OFF) exposure of live human keratinocytes and fibroblasts cells to 5G 3.5 GHz signals at specific absorption rate (SAR) up to 4 W/kg for 24 h impact basal or chemically-induced activity of Heat Shock Factor (HSF), RAt Sarcoma virus (RAS) and Extracellular signal-Regulated Kinases (ERK) kinases, and Promyelocytic Leukemia Protein (PML), that are all molecular pathways involved in environmental cell-stress responses. The main results are (i), a decrease of the HSF1 basal BRET signal when fibroblasts cells were exposed at the lower SARs tested (0.25 and 1 W/kg), but not at the highest one (4 W/kg), and (ii) a slight decrease of As$_2$O$_3$ maximal efficacy to trigger PML SUMOylation when fibroblasts cells, but not keratinocytes, were continuously exposed to the 5G RF-EMF signal. Nevertheless, given the inconsistency of these effects in terms of impacted cell type, effective SAR, exposure mode, and molecular cell stress response, we concluded that our study show no conclusive evidence that molecular effects can arise when skin cells are exposed to the 5G RF-EMF alone or with a chemical stressor.