Entire Function Bounded By Linear Function

Calculus Level 3

Suppose $f: \mathbb{C} \to \mathbb{C}$ is holomorphic. Furthermore, assume that

$|f(z)| \le 5|z|$

for all $z\in \mathbb{C}$ . If $f(1) = 3+4i$ , what is $f(1+i)?$