Arsenic, antimony, and bismuth, three group-V elements which crystallize in the rhomboedral A7 structure, are well-known semimetals. Going from As to Sb to Bi, the unit-cell parameters increase, as well as the strength of the spin-orbit interaction, leading to quantitative differences in the electronic properties of these materials. By means of the standard Hohenberg-Kohn-Sham density-functional approach using the Ceperley-Alder exchange-correlation energy as parametrized by Perdew and Zunger, we have carefully compared the following properties of each semimetal: band structure, electronic density of charge, density of states, and Fermi surface. The role of spin-orbit coupling, which is noticeable in Bi, has been emphasized. The numerical accuracy of the calculation has been strictly controlled, in order to provide reliable comparison between theoretical results and experimental data for the density of states, number of free carriers, and Fermi surface. The good agreement obtained for Fermi surfaces is somewhat unexpected.