The square of a positive number is 24 more than 5 times a number. what is the value of the number?

First, let's construct an algebraic equation to formally find the

Let x represent (the value of) the unknown number. 

x²= 5x + 24 --- This equation shows that the (positive) number's square equals 24 more than 5 times the number.

Now we can solve for x (the number):

                 x² = 5x + 24
  x² - 5x - 24 = 0
(x + 3)(x - 8) = 0
                   x =  -3, 8

Therefore, this means that x (the number ) can be either -3 OR 8. Both will satisfy the description.
Hope this helps!