We present snapshot hyperspectral light field tomography (Hyper-LIFT), a highly efficient method in recording a 5D (x, y, spatial coordinates; θ, φ, angular coordinates; λ, wavelength) plenoptic function. Using a Dove prism array and a cylindrical lens array, we simultaneously acquire multi-angled 1D en face projections of the object like those in standard sparse-view computed tomography. We further disperse those projections and measure the spectra in parallel using a 2D image sensor. Within a single snapshot, the resultant system can capture a 5D data cube with 270 × 270 × 4 × 4 × 360 voxels. We demonstrated the performance of Hyper-LIFT in imaging spectral volumetric scenes.