solve this h=16t^2+100t+5 for hight?

Answer 1

But it's already in the form where height h is the subject!
h=16t²+100t+5
or if you prefer, completing the square for t:
h = (4t + 25/2)² - (5 - (25/2)²)

Did you mean "factorize it"? (that would mean writing t in terms of h, not the other way around)
t = [ -100 ± √100² - 4(16)(5) ] / 2(16)
= [ -25 ± √25² - 4(5) ] / 8
= [ -25 ± √605 ] / 8

h = (t - t1)(t - t2)
h = (t + (25 - √605)/8) (t + (25 + √605)/8)

Answer 2

If you are looking for an equation giving the height of a body
up with initial vertical speed 100 feet/s from an initial position 5 feet the equation should be
h=-16t^2+100t+5
The maximum height is for -32t+100=0 so t= 100/32 s