I would like to hear the reasoning behind why a helmet would be less effective over time.)
The energy-absorbing lining in helmets is made from polystyrene - essentially pretty hard styrofoam. Just like any other synthetic polymer, polystyrene degrades over time, becomes more brittle, crumbles, and loses its ability to absorb energy. This means that a helmet with a degraded energy-absorbing lining won't be nearly as good at absorbing impacts, and in a crash will transfer more crash energy to your brain, causing brain injury.
The speed of this degradation will depend on how the helmet is treated. If you keep your helmet where gasoline fumes are present (like in a garage), or in a hot place, it will degrade faster. If you keep it on a shelf in your bedroom, it will degrade slower.
The recommendation to replace helmets after five years is a rule of thumb. Helmets aren't milk, they won't go bad immediately after the expiration date. But a nearly 20-year-old helmet? No matter how well it's cared for, it's useless as a helmet.
There is also the issue of the helmet's history. Have you owned it since new, so you know that it wasn't crashed, dropped from a height, or otherwise hit? The energy-absorbing lining is one-time-use only. Once a helmet is hit hard (as would happen in a drop from a few feet of height), the polystyrene compresses and won't protect you from another hit in the same place. That's why you should never buy a used helmet.
Also, helmet designs improve over time. Each new generation of helmets has advances not only in protection, but also in comfort, ventilation, wind noise reduction, new features, and so on.
Seriously, do yourself a favor - throw this thing out. Cut off the straps before you do, so someone else won't be tempted to pick it up from the trash and try to use it. There are plenty of helmets that are decent and not too expensive, around $150-$200. You don't have to shell out $800 for a top-end Shoei or Arai. There is no doubt that even a cheapo helmet will be WAY better than this antique one, both in protection and in comfort.