I was terrified of the water until I was six or seven. My parents would take me to swim lessons, and I would cling white-knuckled to the wall and cry and scream the whole time. Then, one day, a swim instructor who was very old school and very no-nonsense literally picked me up and threw me into the shallow end of the pool. Within a few minutes I sort of figured out for myself that I could indeed swim well enough to keep my head above water, I was tall enough to stand up in the shallow end, and by the end of the day I was jumping off the diving board into 9 feet of water.
Now, I certainly don't recommend that you try this with your 5-year-old, but I think for whatever reason, your son has developed this fear and before you can really address the swimming issue, you need to address the fear of the water itself. I think this means ensuring he's comfortable in the water and helping him build his self-confidence in the water. This means that, for now, when he goes in the water, you or your spouse need to go with him. It means lots of encouragement when he does something right. But right now his fear is over-riding any desire to learn to swim. Once he starts seeing the water as a less-scary and more fun, then teaching him to swim will be a lot easier--and that may be a realization he has to come to on his own. Once I became more comfortable in the water, I mastered the basic swimming strokes and skills in no time, and by the time I was in high school I was a lifeguard and a swim instructor in the summer.
As long as there is no immediate danger to your child (ie. you own a pool or live near open water), I would focus my energies on making your son more comfortable in the water, stress that he never goes near the water without mommy or daddy, and always take a life jacket with you when you go near water.