To simplify the expression \((\sqrt{-25} + 2i) + 5i + (9 - \sqrt{-36})\), we will first express the square roots of the negative numbers using complex numbers.
- Simplify \(\sqrt{-25}\):
\[ \sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i \]
- Simplify \(\sqrt{-36}\):
\[ \sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i \]
Now, substituting these simplifications back into the original expression, we have:
\[ (5i + 2i) + 5i + (9 - 6i) \]
Now, combine the terms:
- Combine the \(i\) terms:
\[ 5i + 2i + 5i - 6i = (5 + 2 + 5 - 6)i = 6i \]
- The real part is:
\[ 9 \]
Now we can put both the real and the imaginary parts together:
\[ 9 + 6i \]
Thus, the simplified expression is:
\[ \boxed{9 + 6i} \]