Purpose: To develop and validate an acquisition and processing technique that enables fully self-gated 4D flow imaging with whole-heart coverage in a fixed five-minute scan. Theory and Methods: The data are acquired continuously using Cartesian sampling and sorted into respiratory and cardiac bins using the self-gating signal. The reconstruction is performed using a recently proposed Bayesian method called ReVEAL4D. ReVEAL4D is validated using data from eight healthy volunteers and two patients and compared with a compressed sensing technique, L1-SENSE. Results: Healthy subjects -- Compared to 2D phase-contrast MRI (2D-PC), flow quantification from ReVEAL4D shows no significant bias. In contrast, the peak velocity and peak flow rate for L1-SENSE are significantly underestimated. Compared to traditional parallel MRI-based 4D flow imaging, ReVEAL4D demonstrates small but significant biases in net flow and peak flow rate, with no significant bias in peak velocity. All three indices are significantly and more markedly underestimated by L1-SENSE. Patients -- Flow quantification from ReVEAL4D agrees well with the 2D-PC reference. In contrast, L1-SENSE markedly underestimated peak velocity. Conclusions: The combination of highly accelerated five-minute Cartesian acquisition, self-gating, and ReVEAL4D enables whole-heart 4D flow imaging with accurate flow quantification.