Roots in combination with exponents

Question

I'm looking for a tip on how to simplify this problem.

Answer 1

Hint: Change $(\sqrt 5+2)^{n+2}$ to $(\sqrt 5+2)^n\cdot(\sqrt 5+2)^2$, then combine the $n$-th powers.

Answer 2

Hint: $(\sqrt{5} - 2)(\sqrt{5} + 2) = 1$ by difference of two squares.