Actually, at 5 months the general advice is to hold off on water until 6 months, breast milk or formula is enough hydration at this stage, and extra water can actually fill up her tummy and affect her milk intake. For the cough, a cool-mist humidifier in the room can help loosen the mucus a little while you wait it out. Do check with your PD though, since every baby is different and she's been coughing two weeks already, better to get it assessed properly.