Purely infinite simple real C*-algebras, like their complex counterparts, are classified by their K-theory. Indeed, there are purely infinite simple real C*-algebras (e.g. the exotic Cuntz algebra E_n) whose existence was first identified thanks to K-theory computations. Our long-term goal, in this joint research project with Jeff Boersema, is to construct more concrete models for such C*-algebras. We begin by showing how k-graphs, or higher-rank graphs (which are a higher-dimensional generalization of directed graphs), can give rise to purely infinite simple real C*-algebras. To evaluate whether this class of real k-graph C*-algebras includes E_n, we need to compute the K-theory of real k-graph C*-algebras. To that end, we adapt the spectral sequence studied by D.G. Evans, which converges to the K-theory of a complex k-graph C*-algebra, to the setting of real C*-algebras. Using this spectral sequence, we compute K-theory for several examples of real k-graph C*-algebras. In particular, we exhibit an example of a 7-graph whose C*-algebra is the stabilized exotic Cuntz algebra. This is joint work with Jeff Boersema (and in part, ongoing joint work also with Sarah Browne).