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A respiratory virus is possible. Most of the time, these will present with sneezing, or nasal discharge but a cough is possible. A haiball could also cough an interuption to purring and cause some cough-like activity. An upset stomach with a little gastric reflux is possible. As the acid refluxes it can irritate the throat and cause a cough. Finally, heart disease is possible. If the heart is not functioning effeciently, this can lead to fluid backup in the lungs which can ellicite a cough. While I would not expect this at 5 years of age, it is possible. Allergies are a potential issue as well with asthma being a more severe manifestation. I would try a 1/4 tablet of pepcid AC or tagament twice daily to reduce some stomach acid production. You can also give a teaspoon of maalox twice daily to help coat the system. It may be worth try a hairball remedy as well. I like Laxatone, but there are others. If you feel the signs are more respiratory, then Benedryl (diphenhydramine) at a dose of 1 mg/lb twice daily may be worth a try. Either way, if these tricks are not helping or you are not seeing an improvement, it will be worth a vet visit to investigate some of these potential issues. Xrays and bloodwork are likely tests your vet would start with. I hope this helps and gives you direction.