No matter what your age, exercising with dumbbells is a good way to stay in shape. That said, free weight exercises do offer a number of benefits for seniors specifically.
Overhead press for the shoulder Bent-over rows for the back of the shoulder Front raise for the shoulders and back muscle
When first starting, you will probably feel a little soreness in the muscles and maybe even the joints. Most of the aches should subside within a day or two and will continue to get easier with each ensuing session. If something hurts, stop exercising and lower your weights. Replace any water lost through sweat with either water or an electrolyte sports drink.