A.C.
As someone who also suffers from a phobia, let me tell you a bit about them.
Phobias are an anxiety disorder, not just "ingrained fears." They tend to run in families, so it isn't surprising that other family members have them, as well. They are not necessarily associated with trauma, this is a somewhat out-of-date way of thinking of them. They tend to be related to survival instincts (think about it - the most common phobias are fears of spiders, fears of snakes, fears of blood, enclosed spaces, and heights: all things that were truly life-threatening to humans back in the very beginnings of society), and can be triggered by things that would not affect those who do not suffer from anxiety disorders (such as, oh, a dream).
Five is pretty young for a permanent phobia - at this age, most children have fears that ebb and flow. But since you say this has been an issue since basically his birth, I am inclined to believe it is a true phobia (I am not qualified to diagnose him, however!). There is good news, though, at least for the long run! Phobias can be treated by therapists who specialize in anxiety disorders! I personally do not know how someone would approach this with such a young child (I was an adult when I sought treatment, as was my father when he did), but I would start by calling your local hospital and pediatrician and asking if they can recommend any therapists who work with both children and anxiety disorders.
For the short term, I'm afraid I don't have as much experience. I guess what I would do is think of something you can do to help your son protect himself from the spiders. Telling him his fear is irrational won't help. Would a brighter nightlight help? How about "spider traps" to catch the spiders in case they come out? A special spider-repelling spray? Reassure him that you can catch any spiders he comes across, and that you, as his mommy, will protect him. Sorry, and good luck.