A novel soybean cultivar, designated SG5322NRR, is disclosed. The invention relates to the seeds of soybean cultivar SG5322NRR, to the plants of soybean SG5322NRR and to methods for producing a soybean plant produced by crossing the cultivar SG5322NRR with itself or another soybean variety. The invention further relates to hybrid soybean seeds and plants produced by crossing the cultivar SG5322NRR with another soybean cultivar.