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This paper presents the hardware design of fast and low-cost denoising filters suitable to be exploited in the enabling technologies for Industry 5.0. A novel approximate computing strategy is introduced to reduce the computational complexity of the image denoising operation and to comply with real-time requirements. Firstly, it is demonstrated that the novel approximate approach can be helpfully exploited in the design of reconfigurable denoising filters able to reach image qualities as close as possible to the precise software counterparts. The reconfigurability leads to hardware architectures run-time adaptable to different levels of noise, whereas the adopted approximation strategy limits hardware resources and energy requirements. Quality tests, performed at various image and kernel sizes, and noise standard deviations, demonstrate that the approximate denoising approach presented here reaches PSNR and SSIM comparable with the precise denoise filtering. In comparison with state-of-the-art FPGA-based competitors, the novel filters reduce the resources requirements by up to 70&#x0025;, achieve frame rates up to 35 times higher, and dissipate more than 45&#x0025; lower power. When implemented within the XC7Z7020 FPGA device, a <inline-formula> <tex-math notation="LaTeX">$5\times 5$ </tex-math></inline-formula> filter designed as proposed here denoises <inline-formula> <tex-math notation="LaTeX">$512\times 512$ </tex-math></inline-formula> grayscale images using only 1689 LUTs, 2635 Flip-Flops and 32 DSPs. Moreover, it processes up to 926.8 frames per second, consumes just 63mW &#x0040; 244MHz and, with a noise standard deviation equal to 10, it achieves an average PSNR of <inline-formula> <tex-math notation="LaTeX">$\sim 33$ </tex-math></inline-formula>dB with an average SSIM of &#x007E;0.86.