I think there are some safer and more effective remedies that you have been told. I am very leery of baking soda or Diazanon I think Diazanon is banned now. I am a little disappointed in your vet's advice. Certainly a flea comb is safe. Some of the more effective flea remedies can be applied to a towel, and then the puppy rolled in it. You also need to treat the house and yard with pet safe material. I have used a product called Ovitrol from the vet that kills both fleas and their eggs.
Yes, it is wrong to remove a 5 week old puppy form its mother, but it sounds to me like we should be complementing you for being part of the solution. Bad decisions on the part of the mother's owners are not your fault. Thank you for giving the puppy a home. You will have a tougher time with such a young puppy, but some of the others here and I will give you all the help we can. Start with the sticky at
https://www.askmehelpdesk.com/dogs/i...tml#post251809