We have a right triangle with
a = one leg = 28
b = other leg = 21
c = hypotenuse = 5x
use the pythagorean theorem (a^2+b^2 = c^2) and solve for x
a^2+b^2 = c^2
28^2+21^2 = (5x)^2
784+441 = 25x^2
1225 = 25x^2
25x^2 = 1225
(25x^2)/25 = 1225/25
x^2 = 49
sqrt(x^2) = sqrt(49)
|x| = 7
x = 7 or x = -7
Since the hypotenuse has length 5x meters, this means
5x = 5*7 = 35
or
5x = 5(-7) = -35
Toss out the negative length as it makes no sense.
The only value of x is x = 7
Therefore the final answer is x = 7
