Well maybe not, but (a) your interpretation turns DR 5 into DR 15 when an attack has 3 separate damage types and (b) My approach does not, so I will be sticking with it.
So if I fall in an elemental pool and take 8 fire, 8 cold, 8 acid damage, and have resist 5 fire and cold, I take 3+3+8=14 damage, but if I have resist 5 fire, cold, acid, lightning, thunder, radiant, necrotic, poison, and everything else under the sun (i.e. resist 5 all), I take 3+8+8=19 damage? I don't think that's right. Resist 5 all means resist 5 all, not resist 5 one out of three.