A novel alfalfa variety designated SW5213 and seed, plants and plant parts thereof. Methods for producing an alfalfa plant that comprise crossing alfalfa variety SW5213 with another alfalfa plant. Methods for producing an alfalfa plant containing in its genetic material one or more traits introgressed into SW5213 through backcross conversion and/or transformation, and to the alfalfa seed, plant and plant part produced thereby. Alfalfa seeds, plants, or plant parts produced by crossing alfalfa variety SW5213, or a trait conversion of SW5213, with another alfalfa plant or population. Alfalfa populations derived from alfalfa variety SW5213, methods for producing other alfalfa populations derived from alfalfa variety SW5213 and the alfalfa populations and their parts derived by the use of those methods.
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