Is she has little black specks on her skin, try putting one of those specks on a wet paper towel, if it disolves into a red-ish color then your pup's problem is fleas. At 5 Months I believe it's ok to use repellants although I'm not sure because I don't like using them
If your pooch is flaky then your most likely problem is what you're bathing her with. Some shampoos are just too tough on young pups skin and ends up irritating them. To mitigate the problem use soft shampoo (e.g oatmeal shampoo). Make sure you are brushing before and after the bath to stimulate the oil glands and restore the natural skin oils. Feed fish oils in the pups food to better the condition of the skin too, of course follow the guidelines given so you aren't giving too much.
If you notice bumps or red spots then unfortunately we might be talking about allergies. Only a vet would be able to do tests that would figure out what the allergen is and recommend things to help the itching. I've heard Benedryl is good for allergies though.