The Painleve-V equation has two families of rational solutions, one built from generalized Umemura polynomials and one built from generalized Laguerre polynomials. These solutions have drawn interest because they arise in a variety applications and because their zeros and poles exhibit remarkable geometric structures. We formulate Riemann-Hilbert problems for both families and obtain large-degree asymptotic results using nonlinear steepest-descent analysis. Results for the generalized Umemura solutions are joint with Matthew Satter of the University of Michigan and the results for the generalized Laguerre solutions are joint with Trevor Johnson of the University of Cincinnati.