The five-vertex model is a generalization of the lozenge tiling model, in which certain adjacent dimers interact. It is solvable by Bethe Ansatz. We give an explicit expression for the free energy and surface tension, and show how to parameterize limit shapes explicitly with analytic functions. We similarly solve the "isoradial" version of the model. This talk is based on joint works with de Gier, Watson and Prause.