Max's mistake is in the step where he rewrote 25 as (5^2). This resulted in him raising 5 to the power of 2x-2 instead of (2x-2), which is incorrect.
To solve the equation correctly, we can start with:
5^(x+3) = 25^(x-2)
We can then rewrite 25 as (5^2) and simplify as follows:
5^(x+3) = (5^2)^(x-2)
5^(x+3) = 5^(2x-4)
Now we have the same base on both sides of the equation, so we can equate the exponents:
x + 3 = 2x - 4
Solving for x, we get:
x = 7
Therefore, the solution to the equation is x = 7.