The problem is asking you to multiply two complex numbers, $(10 - 3i)(5 + 2i)$.

Step-by-Step Solution:

1. Use the distributive property (FOIL method) to multiply: $(10 - 3i)(5 + 2i) = 10(5) + 10(2i) - 3i(5) - 3i(2i)$

2. Simplify each term: $= 50 + 20i - 15i - 6i^2$

3. Combine like terms:

   = 50 + 5i - 6i^2$$

4. Recall that $i^2 = -1$: $-6i^2 = -6(-1) = 6$

5. Simplify the expression further: $50 + 5i + 6 = 56 + 5i$

Final Answer:

The product is $56 + 5i$, so the correct option is the first one: $56 + 5i$.

Do you need further details on any of the steps? Here are some related questions:

1. How do you multiply two complex numbers in general?
2. What is the significance of $i^2 = -1$ in complex number multiplication?
3. Can you explain the FOIL method in more detail?
4. What happens when you multiply complex conjugates?
5. How would you add or subtract complex numbers?

Tip: Always remember that $i^2 = -1$ when dealing with imaginary numbers.