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The Industry 5.0 paradigm has a human-centered vision of the industrial scenario and foresees a close collaboration between humans and robots. Industrial manufacturing environments must be easily adaptable to different task requirements, possibly taking into account the ergonomics and production line flexibility. Therefore, external sensing infrastructures such as cameras and motion capture systems may not be sufficient or suitable as they limit the shop floor reconfigurability and increase setup costs. In this paper, we present the technological advancements leading to the realization of ProxySKIN, a skin-like sensory system based on networks of distributed proximity sensors and tactile sensors. This technology is designed to cover large areas of the robot body and to provide a comprehensive perception of the surrounding space. ProxySKIN architecture is built on top of CySkin, a flexible artificial skin conceived to provide robots with the sense of touch, and arrays of Time-of-Flight (ToF) sensors. We provide a characterization of the arrays of proximity sensors and we motivate the design choices that lead to ProxySKIN, analyzing the effects of light interference on a ToF, due to the activity of other sensing devices. The obtained results show that a large number of proximity sensors can be embedded in our distributed sensing architecture and incorporated onto the body of a robotic platform, opening new scenarios for complex applications.