Catalyzes the synthesis of 5,6-dihydrouridine (D), a modified base found in the D-loop of most tRNAs, via the reduction of the C5-C6 double bond in target uridines. a 5,6-dihydrouridine in tRNA + NAD(+) = a uridine in tRNA + H(+) + NADH a 5,6-dihydrouridine in tRNA + NADP(+) = a uridine in tRNA + H(+) + NADPH Belongs to the Dus family. Was originally thought to be involved in the activation of nitrogen assimilatory genes.