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A chunk of 2 x 6 he can use a small back saw to cut a bow on. Add a couple of staggered decks using 1 x 4, 1 x 3, and 1 x 2. A couple of 3" lengths of 1/2" dowel for smoke stacks, and your son has the start of a fleet that floats. Let him bang in nails to fasten things together (predrilling starter holes will make it easier for him to keep them straight), and use the exterior colors of his choice to paint it up.
I remember building one of these with my Dad when I was about that age, and being so proud when it was done I could bust. I was also the envy of the neighbor kids, because I had a "Navy" to carry my toy soldiers around.
If you want to keep it simpler, use a quart or half gallon waxed milk or juice container. Lay it on it's side so the spout is up. Starting just below the spout, mark a line all the way around the carton. Use a sharp knife, or heavy shears, to cut the spout side of the carton away. Assist your son in using a small saw to cut a piece of 1/2" - 3/4" thick balsa wood to fit inside the carton hull. This is to poke dowels into for making masts that can be glued in place and smaller dowel "yard arms" fastened to with twine and glue.
With a 5 year old, keep it simple and have fun.
Len