Let's solve this equation step by step.

First, expand the left side of the equation:

(x-5)(x+5) = x^2 + 5x - 5x - 25
(x-5)(x+5) = x^2 - 25

Now simplify the right side of the equation:

(x-3)^2 + 2 = (x-3)(x-3) + 2
(x-3)^2 + 2 = x^2 - 3x - 3x + 9 + 2
(x-3)^2 + 2 = x^2 - 6x + 11

Now we can set the expanded left side equal to the simplified right side:

x^2 - 25 = x^2 - 6x + 11

Subtract x^2 from both sides to get:

-25 = -6x + 11

Subtract 11 from both sides to get:

-36 = -6x

Divide by -6 to get the solution for x:

x = 6

Therefore, the solution to the equation is x = 6.