Andalusite, Al2SiO5, contains 5- and 6-coordinate aluminum sites, and is a preeminent model for Al-27 NMR spectroscopy. We describe a combined NMR, crystallography, and theory project: single-crystal Al-27 NMR spectra at 298 K, the crystal structure of andalusite at 115 K, and electric field gradient calculations. The low-symmetry 5-coordinate site is a stiff test of the computational methods. In addition, the chemical shift tensor is measured for the 5-coordinate site. The small body of Al-27 NMR data, especially for rare 5-coordinate sites, inspires the calculation of NMR parameters. We explore the accuracy of two approaches for Al-27 EFG calculations: first, ab initio molecular orbital calculations of small clusters embedded in an array of point charges; second, full-potential linearized augmented plane wave density functional calculations of the crystal. The agreement between the experimental EFG orientation and that from the full-crystal density functional theory is remarkably close, differing by only 0.17 degrees for the 6-coordinate site and 1.56 degrees for the 5-coordinate site. The calculated value of C-q is in error by -0.254 MHz for the 5-coordinate site. The embedded cluster molecular orbital results are significantly less accurate, with orientation errors exceeding 45 degrees.