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Aims. To derive the thermal inertia of 2008 EV$_5$, the baseline target for the Marco Polo-R mission proposal, and infer information about the size of the particles on its surface. Methods. Values of thermal inertia are obtained by fitting an asteroid thermophysical model to NASA's Wide-field Infrared Survey Explorer (WISE) infrared data. From the constrained thermal inertia and a model of heat conductivity that accounts for different values of the packing fraction (a measure of the degree of compaction of the regolith particles), grain size is derived. Results. We obtain an effective diameter $D = 370 \pm 6\,\mathrm{m}$, geometric visible albedo $p_V = 0.13 \pm 0.05$ (assuming $H=20.0 \pm 0.4$), and thermal inertia $\Gamma = 450 \pm 60$ J/m2/s(1/2)/K at the 1-$\sigma$ level of significance for its retrograde spin pole solution. The regolith particles radius is $r = 6.6^{+1.3}_{-1.3}$ mm for low degrees of compaction, and $r = 12.5^{+2.7}_{-2.6}$ mm for the highest packing densities., Comment: 16 pages, 8 figures; accepted for publication in Astronomy & Astrophysics