Let's simplify the given expression:

(а+1)^2 = a^2 + 2a + 1

3(a-1)^2 = 3(a^2 - 2a + 1) = 3a^2 - 6a + 3

-5(a+1)(a-1) = -5(a^2 - 1) = -5a^2 + 5

Adding everything together:
(a^2 + 2a + 1) + (3a^2 - 6a + 3) - (5a^2) + 5)

Simplifying further:
a^2 + 2a + 1 + 3a^2 - 6a + 3 - 5a^2 + 5
= a^2 + 3a^2 - 5a^2 + 2a - 6a + 1 + 3 + 5
= -a^2 - 4a + 9

Therefore, the simplified expression is -a^2 - 4a + 9.