$f(f(x)) = 4x+3$; $\forall x \in \mathbb{N}$ and $f(5^k) = 5^k \times 2^{k-2} + 2^{k-3}$. Find $f(2015)$.

Question

For all positive integer $x$, $f(f(x)) = 4x+3$; and for ONLY ONE positive integer $k$, $f(5^k) = 5^k \times 2^{k-2} + 2^{k-3}$. Find $f(2015)$.

Dont know where to start. Any hint will be helpful. Dont give full solution.
Source: BdMO 2016 Dhaka regional Higher Secondary.

Answer 1

Sort of a hint: Since $f(f(x))$ is linear, I suspect that so is $f(x)$. I assumed that $f(x) = ax+b$ and was able to get the answer.

Answer 2

Hint 1: f(x) is injective

Hint 2:$2017=503\cdot 4+3,503=4\cdot 125+3$