Those tests don't account for different body types.
I know several 5'8" athletic women (full sport scholarships, basketball and volleyball) who were heavier than you, but were broad built.
Of course, I know several model types at 5'8" who weighed in around 115lbs., totally no reserve, always getting flus or colds, no resistance, and hand to eat a regular schedule.
Healthy is more important than looking skinny for the boyz. At your weight, average built, you're about right in weight.
Get in shape, don't bother obsessing about your weight.