Measuring the shape (coordinates x, y, z ) and spectral characteristics (wavelength-dependent reflectance R (λi)) of macroscopic objects as a function of time (t) is of great interest in areas such as medical imaging, precision agriculture, or optical sorting. Here, we present an approach that allows to determine all these quantities with high resolution and accuracy, enabling measurement in five dimensions. We call this approach 5D hyperspectral imaging. We describe the design and implementation of a 5D sensor operating in the visible to near-infrared spectral range, which provides excellent spatial and spectral resolution, great depth accuracy, and high frame rates. The results of various experiments strongly indicate the great benefit of the new technology.