5 week old puppy

Definitely not, dogs are actually lactose intollerent and cow milk contains lactose so can have some very nasty (and messy) consequences.
At 5 weeks the pups should be well onto it's way to being weaned. You can feed either canned puppy food or some soaked puppy dry food.
To soak dry food you just add half the amount of warm (not boiling) water that you do dry food. So 1 cup of dry needs half a cup of water.
Leave it to soak for around half an hour and then serve.

You can still give the pup milk (either on its own or soaked in the dry food) but it must be lactose free. Goats milk is commonly used for those who cannot get hold of puppy milk supplements and it is perfectly safe. When you give the pup the new milk make sure you do so in very small amounts and build it up to avoid digestive problems, dog's can't adjust to sudden changes in diet as well as we can.

Thank you