Diseased heart valves perturb normal blood flow with a range of hemodynamic and pathologic consequences. In order to better stratify patients with heart valve disease, a comprehensive characterization of blood flow including turbulent contributions is desired. In this work we present a framework to efficiently quantify velocities and Reynolds stresses in the aorta in-vivo. Using a highly undersampled 5D Flow MRI acquisition scheme with locally low-rank image reconstruction, multipoint flow tensor encoding in short and predictable scan times becomes feasible (here, 10 minutes), enabling incorporation of the protocol into clinical workflows. Based on computer simulations, a 19-point 5D Flow Tensor MRI encoding approach is proposed. It is demonstrated that, for in-vivo resolution and signal-to-noise ratios, sufficient accuracy and precision of velocity and turbulent shear stress quantification is achievable. In-vivo proof of concept is demonstrated on patients with a bio-prosthetic heart valve and healthy controls. Results demonstrate that aortic turbulent shear stresses and turbulent kinetic energy are elevated in the patients compared to the healthy subjects. Based on these data, it is concluded that 5D Flow Tensor MRI holds promise to provide comprehensive flow assessment in patients with heart valve diseases.