The complex conjugate of a complex number $a + bi$ is obtained by changing the sign of the imaginary part. For the complex number $-5 + 3i$, the complex conjugate is:

$-5 - 3i$

Let me know if you'd like more details on complex conjugates or have further questions.

Here are some related questions to explore:

1. What is the modulus of $-5 + 3i$?
2. How do you find the argument (angle) of $-5 + 3i$?
3. How does the complex conjugate relate to the modulus of a complex number?
4. What is the result of multiplying $-5 + 3i$ by its conjugate?
5. How do complex conjugates behave in division of complex numbers?

Tip: The product of a complex number and its conjugate always yields a real number, specifically the square of the modulus.