First, you must know what 5^2 and 5^3 are equal to.
5^2 = 5 * 5 = 25
5^3 = 5 * 5 * 5 = 125
If x^2 is equal to 25, x = 5. If x^2 is greater than 25, x > 5. If x^2 is less than 25, then x < 5.
If x^3 is equal to 125, x = 5. If x^3 is greater than 125, x > 5. If x^3 is less than 125, then x < 5.
x^3 = 15; x < 5
x^2 = 25; x = 5
x^3 = 36; x < 5
x^2 = 49; x < 5
x^2 = 50; x > 5
x^3 = 125; x = 5