Will patients with congestive heart failure die within 5 years?

Not necessarily. With good healthcare and, good lifestyle choices (limit salt, weight loss, no smoking, etc) people can live long lives even with a history of chf. There are excellent medications to help the heart beat more efficiently, decrease fluid, and help people feel much better.
Some; not usually. Modern treatment has changed the game completely, but requires seeing a heart failure specialist. Also strongly dependent of cause of heart failure, e.g., coronary disease, viral, hypertensive, drug induced, valvular, metabolic, inflitrative, etc., and whether there are reversible components. Need to see a physician who manages heart failure; ask your doctor to whom he would send his mother.