One of my 5y.o. kids sweats a lot under their arms. they are not only moist when cool, but stink why?

Genes: Sweat glands are regulated by hormones that are in turn regulated genetically. This is assuming your child is, otherwise, healthy. If your child has a metabolic disorder, he may excrete certain chemicals through his sweat that cause it to have unusual odor. But this is not to be taken as a sole sign of disease. There must be other symptoms suggestive of a metabolic disorder.

Diet: Sometimes diet can affect the sweat odor. I have had two different cases where diet changes solved the problem. One was a child eating a lot of dairy. The other was affected by too much red meat. Dietary changes can make big differences in our health. Sometimes by just looking at the most popular items in a child's diet and eliminating them for a week or two you may see a significant change.