First, we need to simplify the expressions:

(x+3)(x^2-4x+7) = x(x^2) + 3(x^2) - 4x^2 + 7x + 3(-4x) + 3(7)
= x^3 + 3x^2 - 4x^2 + 7x - 12x + 21
= x^3 - x^2 - 5x + 21

(x^2-5)(x-1) = x^2(x) - 5(x) - 1(x^2) + 5(1)
= x^3 - 5x - x^2 + 5

Now, we can subtract the two simplified expressions:

(x+3)(x^2-4x+7) - (x^2-5)(x-1) = (x^3 - x^2 - 5x + 21) - (x^3 - 5x - x^2 + 5)
= x^3 - x^2 - 5x + 21 - x^3 + 5x + x^2 - 5
= -2x + 16

Therefore, the solution is -2x + 16.