Cleaning your 5-week old puppy is not much different than cleaning him just a week ago. Until your puppy is about 2 months old, he should not need a deep cleaning bath. However, your puppy is regulating his body temperature much better than he has so far. So you can get him wet and you can submerge him in a bath if you need to. You will still need to make sure he is nice and warm and dry once his bath time is over. If you don't need to submerge him in a bath, it is still a good idea to simply wipe him down from head to toe with a warm, wet washcloth rather than submerging him in a tub or sink full of water.
Your 5-week-old puppy might be a little nervous about the sound of running water. If you get your puppy wet, he may shiver and be extremely cold even though his body is doing a better job of regulating his temperature. Try to make cleaning quick and easy and get him dry and warm again as quickly as you can.