Five years is a fairly typical life-time for a car battery.
They deteriorate rapidly if left partially discharged for prolonged periods of time, and the life can be significantly prolonged by ensuring that the battery is fully charged every day that is has been in heavy use in such a manner that the normal motor vehicle "float charge" system has left it partially discharged.
Unfortunately, the float charge system is not ideal - the longest lifetimes for non-sealed lead-acid batteries are obtained if the battery is fully discharged one day then fully charged again the next day, with regular checks being made on the electrolyte level combined with "topping up" with distilled water where necessary.
. Such treatment can enable a lead-acid battery to last several times longer than normal with minimal deterioration, however the procedure is normally only followed with equipment like marine communications installations and is not well suited to normal motor vehicles (as they have no provision for either fully discharging them, nor conveniently fully recharging them on alternate days. . Best wishes - Majikthise. .
It depends on the battery, the climate, and how the car is used.
There is a new technology in car batteries called Absorbed Glass Mat or AGM batteries. Instead of being flooded with sulphuric acid the acid in these batteries are abosrbed into fiberglass mats between the plates. Even when shot with a bullet they do not leak acid. Only in unusual circumstances to they even produce hydrogen that needs to be vented. The most common use of AGM batteries is in cars with the battery in the trunk or under the back seat to avoid the smell of battery acid.
AGM batteries are better in almost every way than acid flooded batteries. AGM batteries last longer, are lighter, and are safer. The drawbacks are that they are more expensive and they can not be rapidly charged. An acid flooded battery can be charged in under an hour but an AGM battery can only be slow charged.
I've been averaging 3-4 years from my acid flooded batteries and 8 years from AGM batteries. Whenever possible I specify AGM car batteries though they are not available in all sized and capacities.
Yes - deep discharging causes too much of the active materials on the plates ("Soft Spongy" Lead on the Negative plates, and Lead Dioxide on the Positive plates) to be converted to Lead Sulphate. The terminal voltage drops to near zero, charging becomes either non-existent or at best very inefficient, and the Lead Sulphate converts to a hard crystalline form which cannot be converted back to the fully charged active materials ..... ..... a condition known as "sulphation", that pretty well marks the end of the battery's useful life.
Another thing that greatly reduces the life of a typical car battery is deep cycling it. Discharging a car battery to almost dead by leaving lights on all night can drastically reduce the battery's life. There are special lead acid batteries designed for deep cycling that are not harmed by this.
2 years average