With just a 5 day dose of prednisone, tapering is not necessary. But, as you have found it does affect your blood sugar and blood pressure.
The aim of this short course of therapy is to calm the inflammation in your airways.
Did you have the cough as the result of a cold or influenza? If so, this will hopefully take care of it. If it persists, you should be evaluated for any underlying respiratory condition like asthma or COPD so you can get a long-term treatment.
How is the cough now?