You already have good advice but keep the cats separate and do not give him the over the counter flea stuff- wait till you (and the kitten of course) see your vet.It is usually unsafe to use anything on a kitten under 8 wks of age! You did the right thing in giving him a bath - Dawn is also good for bathing a cat. But keep him warm and if you bottle fed him, make sure you help him eliminate as his feline mama would do. At 5 wks, he may already be doing it tho - you did not mention that. If he is not, use a soft cotton ball or paper to rub him in the place he eliminates from. (Mama cats usually lick their babies but you can find an alternative
He could be very anemic since fleas can kill a kitten - they suck so much blood! In picking off the fleas, some people will place some Vaseline on the base of the comb's teeth to stop the fleas from escaping the comb. (Fleas alas are not stupid and head for the dry areas)
I hope he'll be OK. The anemia can be very dangerous- did you notice any reddish color in the water?
Your vet will likely do a HEMATOCRITor PACKED CELL VOLUME (PCV) test to determine degree of anemia. The hematocrit or PCV reflects the percentage of red blood cells that should be present in a sample of blood. In cats the normal range is 24 to 45. Blood transfusion is often used at values of 20 or less. Some vets use Capstar, a relatively new fast-acting flea-killing tablet with no known side effects for mammals. It is labeled for use in animals weighing 2 lbs or more and is excellent in serious situations. Vets tend to call the serious situations Flea Anemia.
I hope your kitten will be fine! Please let us know what happens and best of luck to you and him!