To solve the equation (7x-24)(0.5)^4 = 5^6, we can start by simplifying both sides of the equation.

First, let's simplify the left side of the equation:
(7x-24)(0.5)^4 = (7x-24)(0.0625) = 0.4375(7x-24)

Now, let's simplify the right side of the equation:
5^6 = 5 * 5 * 5 * 5 * 5 * 5 = 15625

So, the equation becomes:
0.4375(7x-24) = 15625

Next, let's distribute 0.4375 to (7x-24):
0.4375 * 7x - 0.4375 * 24 = 15625

Simplifying further:
3.0625x - 10.5 = 15625

Now, let's isolate the variable x by adding 10.5 to both sides of the equation:
3.0625x = 15635.5

Finally, divide both sides of the equation by 3.0625 to solve for x:
x = 15635.5 / 3.0625

Using a calculator, we find that x ≈ 5099.19.

Therefore, the solution to the equation (7x-24)(0.5)^4 = 5^6 is x ≈ 5099.19.