To simplify this expression, we need to first factor the numerator and denominator:

Factor the numerator:
x^2 - 10x + 25
= (x - 5)(x - 5)
= (x - 5)^2

Factor the denominator:
3x + 12
= 3(x + 4)

2x - 10
= 2(x - 5)

x^2 - 16
= (x + 4)(x - 4)

Now, our expression becomes:

((x - 5)^2) / (3(x + 4)(x - 5)) ÷ (2(x - 5) / (x + 4)(x - 4))

Next, we rewrite the expression by multiplying by the reciprocal of the second fraction:

((x - 5)^2) / (3(x + 4)(x - 5)) * ((x + 4)(x - 4) / 2(x - 5))

Now, we cancel out common factors:

(x - 5) / 3 (x + 4) (x - 4) / 2

Which simplifies to:

(x - 5)(x + 4)(x - 4) / 6

So, the simplified expression is:

(x - 5)(x + 4)(x - 4) / 6