In this paper, we propose to extend the state-of-the-art BM3D image denoising filter to light fields, and we denote our method LFBM5D. We take full advantage of the 4D nature of light fields by creating disparity compensated 4D patches which are then stacked together with similar 4D patches along a 5^th dimension. We then filter these 5D patches in the 5D transform domain, obtained by cascading a 2D spatial transform, a 2D angular transform, and a 1D transform applied along the similarities. Furthermore, we propose to use the shape-adaptive DCT as the 2D angular transform to be robust to occlusions. Results show a significant improvement in synthetic noise removal compared to state-of-the-art methods, for both light fields captured with a lenslet camera or a gantry. Experiments on Lytro Illum camera noise removal also demonstrate a clear improvement of the light field quality.