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Background: Free-running cardiac and respiratory motion-resolved whole-heart five-dimensional (5D) cardiovascular magnetic resonance (CMR) can reduce scan planning and provide a means of evaluating respiratory-driven changes in clinical parameters of interest. However, respiratory-resolved imaging can be limited by user-defined parameters which create trade-offs between residual artifact and motion blur. In this work, we develop and validate strategies for both correction of intra-bin and compensation of inter-bin respiratory motion to improve the quality of 5D CMR. Methods: Each component of the reconstruction framework was systematically validated and compared to the previously established 5D approach using simulated free-running data (N = 50) and a cohort of 32 patients with congenital heart disease. The impact of intra-bin respiratory motion correction was evaluated in terms of image sharpness while inter-bin respiratory motion compensation was evaluated in terms of reconstruction error, compression of respiratory motion, and image sharpness. The full reconstruction framework (intra-acquisition correction and inter-acquisition compensation of respiratory motion [IIMC] 5D) was evaluated in terms of image sharpness and scoring of image quality by expert reviewers. Results: Intra-bin motion correction provides significantly (p