Solve: (x-2)5^x = 5^(x+2)

To solve the given equation, we need to get rid of the exponents. We have (x - 2)5^x = 5^(x + 2).

First, let's simplify by using the properties of exponents:
(x - 2)5^x = 5^x * 5^2
(x - 2)5^x = 5^(x + 2)

Next, let's cancel out the common factor of 5^x on both sides of the equation:
(x - 2) = 5^2
(x - 2) = 25

Now, let's solve for x:
x - 2 = 25
x = 25 + 2
x = 27

Therefore, the solution to the equation (x-2)5^x = 5^(x+2) is x = 27.