How do I get fleas off my 5 week old puppy?

Firstly, check the puppy's mom for fleas.

Secondly, bathe the pup in warm water with dishwashing detergent added. Be very careful not to let the puppy get a chill, it can kill them this young. Dry the puppy very thouroughly to keep it warm.

Thirdly, launder the bedding with bleach to kill fleas and larvae in it.

If the mom has fleas, you have a good deal of work ahead of you.