It is extremely important for senior golfers to keep their left arm straight during their backswing as doing this allows you to make a great connection with the golf ball and secondly you will generate maximum club head speed when you swing and therefore hit the ball the maximum distance that you can.
As you address the golf ball, you should have a straight left arm if you are a right handed golfer. As you swing the club head away from the golf ball on your backswing, work on pushing your hands away from your body to keep your left arm fully extended out from your body and straight. As you do this, the club head will travel at the maximum distance possible away from your body, giving you the widest possible swing arc. The wider your swing arc, the further the club head has to travel around you as you swing it, so the more time you have to build speed into the movement. The faster you swing the club head through impact, the more speed will be transferred into the ball and therefore the further you will hit the golf ball.
Keeping your left arm straight also affects the connection that you get between the club head and the golf ball. If you bend you left arm during your golf swing, you are shortening the distance between yourself and the club head. At the start of your swing the club head is at a maximum length away from you, so if you shorten this distance and then try to return the club head back to the golf ball, the club head will now be closer to you and as a result it will strike the top of the golf ball. Keeping your left arm straight during your backswing allows you to swing the club head back down to the golf ball at the height it started at so that you strike the ball well.
To encourage a straight left arm during your backswing, work on achieving the following:
At set up, create a straight line from your left shoulder down your straight left arm to your left hand and then down the club shaft to the club head. Work on pushing your hands away from your torso as you swing back, rather than pulling your hands in towards your body. To get the feeling of doing this, take a resistance band and place one end of it under your left foot so that it wraps up the outside of your foot. Now hold the other end in your hands as you hold the golf club. As you swing the club away from the golf ball on your backswing, stretch the resistance band away from you and this will extend your left arm and teach you how to push your hands away from your body.
If you do not have a resistance band, you could always use a large plastic bottle that you could cut either end off just to leave the cylindrical body. Slide this over your left elbow and now make your backswing - you will not be able to bend your left arm due to the bottle sleeve. HOWEVER, do not try to swing through with this on as your left elbow needs to bend on your follow through so only use this to help get the feel of keeping your arm straight on your backswing.