A 5 month old baby can be given some Benadryl for allergies but you should only give the 5 month old baby Benadryl under a doctors advise.
The doctor can tell you exactly how much of a dosage you can give your baby of Benadryl.
You would need to cut the Benadryl pill up to a small size and only give the 5 month old baby very little of it or they can easily overdose on it.
Children under 2 years old should only be given the recommended dosage of Benadryl under a doctors advise.
They do make child specific Benadryl but not for infants or those under 6 years old.