We study a system of discrete Painlevé V equations via the Riemann-Hilbert approach. We begin with an isomonodromy problem for dPV, which admits a discrete Riemann-Hilbert problem formulation. The asymptotics of the discrete Riemann-Hilbert problem is derived via the nonlinear steepest descent method of Deift and Zhou. In the analysis, a parametrix is constructed in terms of specific Painlevé V transcendents. As a result, the asymptotics of the dPV transcendents are represented in terms of the PV transcendents. In the special case, our result confirms a conjecture of Borodin, that the difference Schlesinger equations converge to the differential Schlesinger equations at the solution level.
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