Catalyzes the NADH/NADPH-dependent oxidation of L-idonate to 5-ketogluconate (5KG). L-idonate + NADP(+) = 5-dehydro-D-gluconate + H(+) + NADPH L-idonate + NAD(+) = 5-dehydro-D-gluconate + H(+) + NADH Binds 2 Zn(2+) ions per subunit. Carbohydrate acid metabolism; L-idonate degradation. Belongs to the zinc-containing alcohol dehydrogenase family.