1. The problem states that $f$ is an odd function, $f(3) = -2$, and the point $(-3, 5a - 13)$ lies on the curve of $f$. We need to find the value of $a$. 2. Recall the definition of an odd function: for all $x$, $f(-x) = -f(x)$. 3. Given $f(3) = -2$, by the odd function property, $f(-3) = -f(3) = -(-2) = 2$. 4. The point $(-3, 5a - 13)$ lies on the curve, so $f(-3) = 5a - 13$. 5. Equate the two expressions for $f(-3)$: $$5a - 13 = 2$$ 6. Solve for $a$: $$5a = 2 + 13$$ $$5a = 15$$ $$a = \frac{15}{5} = 3$$ 7. Therefore, the value of $a$ is 3. Final answer: $a = 3$