1. **State the problem:** Multiply and simplify the complex numbers $(-2 - 3i)$ and $(-5 - 2i)$. 2. **Recall the formula:** To multiply two complex numbers $(a + bi)(c + di)$, use the distributive property: $$ (a + bi)(c + di) = ac + adi + bci + bdi^2 $$ Remember that $i^2 = -1$. 3. **Apply the formula:** Let $a = -2$, $b = -3$, $c = -5$, and $d = -2$. $$ (-2 - 3i)(-5 - 2i) = (-2)(-5) + (-2)(-2i) + (-3i)(-5) + (-3i)(-2i) $$ 4. **Calculate each term:** $$ (-2)(-5) = 10 $$ $$ (-2)(-2i) = 4i $$ $$ (-3i)(-5) = 15i $$ $$ (-3i)(-2i) = 6i^2 $$ 5. **Substitute $i^2 = -1$ and simplify:** $$ 6i^2 = 6(-1) = -6 $$ 6. **Combine all terms:** $$ 10 + 4i + 15i - 6 = (10 - 6) + (4i + 15i) = 4 + 19i $$ **Final answer:** $$ \boxed{4 + 19i} $$