In such a case we have to reassess the patient.
Thanks and welcome to healthcare magic.
After taking the antibiotics there is no permanent relief, one has to revise the diagnosis .
Couh persisting for 5 weeks and no relief with antibiotics TB infection should be kept in mind.
Thorough investigation must be taken up in those lines and diagnosis confirmed or ruled out.
Even if it is not TB, decide whether correct antibiotic given in correct dose and for required duration.
Without seeing the patient and without examining it is difficult to say the exact diagnosis from history alone.
Age of the patient , diagnosis and antibiotic used and the dose were not mentioned in your query.
Better consult a pediatrician
and if you have already consulted go for a second opinion
Hope this answer suits your purpose.
Please feel free to ask further queries if required.