This paper considers a compressive multi-spectral light field camera model that utilizes a one-hot spectral-coded mask and a microlens array to capture spatial, angular, and spectral information using a singlemonochrome sensor. We propose a model that employs compressed sensing techniques to reconstruct thecomplete multi-spectral light field from undersampled measurements. Unlike previous work where a lightfield is vectorized to a 1D signal, our method employs a 5D basis and a novel 5D measurement model, hence,matching the intrinsic dimensionality of multispectral light fields. We mathematically and empirically showthe equivalence of 5D and 1D sensing models, and most importantly that the 5D framework achieves or-ders of magnitude faster reconstruction while requiring a small fraction of the memory. Moreover, our newmultidimensional sensing model opens new research directions for designing efficient visual data acquisitionalgorithms and hardware.