It will work, and there is good advice above. Boil the water for a while first---I'd probably go half an hour or so. This is to sanitize it (which only needs a few minutes) and to deoxygenate it (which may take longer, I don't have a good number, so I'd just boil as long as is convenient). Cover and cool it, and I'd suggest siphoning it in to avoid splashing.
Before doing this, though, test it on a small quantity. I'd draw a few ounces of beer out and put something like 2 ounces (1/4 cup) in a glass. Taste it. Add a teaspoon (1/6 ounce) or maybe 1/2 teaspoon (1/12 ounce) of water, stir it up, and taste again. If it still tastes good, add another teaspoon and try again. Note when it starts tasting worse and try to remember where you thought it tasted best.
Then, start over with a couple ounces of pure beer and add what you thought was the best amount of water and try again. Make sure you're happy with that. If so, scale it up and dilute in that ratio. If you have 4 gallons, then that's 512 ounces, so a 2 ounce sample is 1/256 of that, or about 0.4%. So whatever dilution you liked best, multiply by 256 to figure out the amount of water to add to the whole batch. That works out to about 43 ounces (5.3 cups) per teaspoon added to your sample.
Anyway, that's how I'd do it. But I'd be cautious about this---you have 4 gallons of very strong, probably very expensive beer on your hands. It'd be a shame to spoil it trying to stretch it to 5 gallons. I'd be strongly inclined to "suffer" with a smaller number of bottles of full-strength beer. With something that strong, you could also look into smaller bottles since you may only want an 6-8 ounce serving in one go. I'm not sure how feasible that is, but a few cases of 6-oz Coke bottles full of beer would be pretty cool.