$a_n = c_1 r_1^n + c_2 r_2^n$ where $r_1, r_2$ are roots of $r^2 - 5r + 6 = 0$

$a_n = c_1 e^{5n} + c_2 e^{-6n}$

$a_n = c_1 \sin(5n) + c_2 \cos(6n)$

$a_n = 5^n - 6^n$