My is coughing with yellow sputum for 10dys. Last 2dys no sputum, she's coughing less but sweating. No fever all time. Is it pneumonia, bronchitis or?

Pneumonia. Several considerations are possible given symptoms of fever, cough and yellow sputum production, but pneumonia (PNA) should be strongly considered in a 65YO person with these persistent symptoms. If you are a smoker your risk for PNA and acute on chronic bronchitis increases. If you have a lot of sinus congestion then sinusitis may also be considered as a cause of your symptoms.
Coughing / sputum. The reduction of coughing and sputum are good signs. There was no fever, so probably this was a case of bronchitis. If there was a chest xray during the assessment of this case, it may have been read as normal. What was the treatment? It sounds like the case is improving. Good to know.
Can be either. With an elder lady, depending upon history of lung disease or smoking etc, she can have either. If she doesn't feel well, she should be examined by her doctor, possibly get a chest X Ray and possibly some other tests to get treatment. to make her feel better.
Normal. I don't know if this is you or someone else. The yellow sputum is just inflammatory cells and the cough helps clear the lungs so is a natural protection. Cough medicine does not work well but if the cough persists, an ashtma inhaler will alleviate it until the cough is better. An xray will tell if it is pneumonia and it could be a walking pneumonia, we call it bronchitis if it isn't a pneumonia.
Could be both. This collection of symptoms requires a thorough history and exam . You could indeed have pneumonia or bronchitis. Please get examined at an emergency room.