In this paper, a convolutional neural network for joint image demosaicing, denoising, deblurring, super-resolution and clarity enhancement is proposed. The network inputs are four-channel Bayer CFA image (R, G, G, B) and three channels of the same size containing distortions maps, namely, noise level map, blur level map, and clarity degradation map. It is shown that the designed network FiveNet can effectively process images with the mix of five different distortions. It is also demonstrated that adding clarity enhancement into the processing chain can additionally increase image quality (by up to 3-4 dB in PSNR). A small dataset ClarityDegr120 of color images with different clarity degradations and enhancements is designed using images processed by FiveNet. Mean opinion scores (MOS) for the test set are collected. The MOS prove that clarity enhancement can significantly increase image visual quality. A comparative analysis using the MOS demonstrates a low correspondence between image quality metrics and human perception for the clarity enhancement task.