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We investigate the low temperature magnetic properties of a S=5/2 Heisenberg kagome antiferromagnet, the layered monodiphosphate Li_{9}Fe_{3}(P_{2}O_{7})_{3}(PO_{4})_{2}, using magnetization measurements and ^{31}P nuclear magnetic resonance. An antiferromagnetic-type order sets in at T_{N}=1.3  K and a characteristic magnetization plateau is observed at 1/3 of the saturation magnetization below T^{*}∼5  K. A moderate ^{31}P NMR line broadening reveals the development of anisotropic short-range correlations concomitantly with a gapless spin-lattice relaxation time T_{1}∼k_{B}T/ℏS, which may point to the presence of a semiclassical nematic spin-liquid state predicted for the Heisenberg kagome antiferromagnetic model or to the persistence of the zero-energy modes of the kagome lattice under large magnetic fields.