Let's expand the expression step by step:

5(a-4)² = 5(a-4)(a-4) = 5(a² - 4a - 4a + 16) = 5(a² - 8a + 16) = 5a² - 40a + 80

(a-4)(7-2a) = a(7) - a(2a) - 4(7) + 4(2a) = 7a - 2a² - 28 + 8a = 15a - 2a² - 28

Finally, we have:

5(a-4)² - (a-4)(7-2a) + 20a²
= 5a² - 40a + 80 - (15a - 2a² - 28) + 20a²
= 5a² - 40a + 80 - 15a + 2a² + 28 + 20a²
= 5a² - 15a + 2a² + 20a² - 40a + 80 + 28
= 27a² - 55a + 108

So, the final simplified expression is 27a² - 55a + 108.