Just because something worked doesn't mean it wasn't a placebo.
Sure, the vitamin D in his blood may increase, but the anecdote of "it works" is about him getting sick less. And that could be a placebo effect and any sake pill would have had the same effect.
And the placebo effect can happen even when the person knows it's a fake pill.
What's important is that vitamin D is fat-soluble and will accumulate in your body. So if you do 5,000 IU/day for ever, your serum levels will likely just go up and up. 5,000 IU per day is not (as the other comments point out) anywhere a "megadose" — most people produce thousands of IU per hour when out in full sunlight — but it can eventually cause problems, including kidney stones and bone mineral density loss. (There's evidence that taking vitamin K2 together with the vitamin D helps maintain bone density.)
What's better is to do this for a while, then test your blood, then change the dose accordingly. Since the lag time is measured in weeks, it may take a while to find the right dose.
That reads as "four to five thousand IUs."