To simplify the given expression:

3 - 2(5 - x)(x - 5) - 2(5 + x)^2

First, simplify the terms inside the parentheses:

3 - 2(-x)(-5) - 2(5 + x)^2
3 - 2(x)(-5) - 2(25 + 10x + x^2)

Now, distribute the negative sign and simplify further:

3 + 10x - 2(25 + 10x + x^2)
3 + 10x - 50 - 20x - 2x^2

Combine like terms:

-2x^2 - 10x - 47

Therefore, the simplified expression is:

-2x^2 - 10x - 47.