What is a healthy weight for a 5'8'' female?

There is a range: YEARS ago, when I was in medical school, we were taught that ideal weight was 100# for a woman 5 feet in height; then add 5 pounds per inch, so for 5'8"--140 pounds. This is pretty close. But you need to make allowances for muscularity, fitness, genetically bigger bones, etc., so I would say a range of 135 to 150 pounds would be ideal. You could also aim for 22-26% body fat. Good wishes:)