4. For the function $f(x)$, it is known that it is odd, i.e., $f(-x) = -f(x)$ for every real $x$. Additionally, it is known that for every $x$, $f(x+5) = f(x)$, and also $f(1 / 3) = 2022$, and $f(1 / 2) = 17$. What is the value of

$$
f(-7) + f(12) + f\left(\frac{16}{3}\right) + f\left(\frac{9}{2}\right) ?
$$
Answer: 2005.

Solution. Let's find the values of $f(-7)+f(12)$, $f\left(\frac{16}{3}\right)$, and $f\left(\frac{9}{2}\right)$ separately.

- $f(-7)+f(12)=f(-7+5)+f(12-2 \cdot 5)=f(-2)+f(2)=0$;
- $f\left(\frac{16}{3}\right)=f\left(5+\frac{1}{3}\right)=f\left(\frac{1}{3}\right)=2022$.
- $f\left(\frac{9}{2}\right)=f\left(5-\frac{1}{2}\right)=f\left(-\frac{1}{2}\right)=-f\left(\frac{1}{2}\right)=-17$

The answer is $0+2022-17=2005$.