To simplify the expression \((-6 + \sqrt{5})(-9 - \sqrt{5})\), we will use the distributive property (also known as the FOIL method for binomials).
Let's expand the expression step by step:
\[ (-6 + \sqrt{5})(-9 - \sqrt{5}) = (-6)(-9) + (-6)(-\sqrt{5}) + (\sqrt{5})(-9) + (\sqrt{5})(-\sqrt{5}). \]
Now, we calculate each term:
- \((-6)(-9) = 54\)
- \((-6)(-\sqrt{5}) = 6\sqrt{5}\)
- \((\sqrt{5})(-9) = -9\sqrt{5}\)
- \((\sqrt{5})(-\sqrt{5}) = -5\)
Now we combine all the terms:
\[ 54 + 6\sqrt{5} - 9\sqrt{5} - 5. \]
Now, we can combine like terms:
- The constant terms: \(54 - 5 = 49\)
- The terms involving \(\sqrt{5}\): \(6\sqrt{5} - 9\sqrt{5} = -3\sqrt{5}\)
Putting it all together, we get:
\[ 49 - 3\sqrt{5}. \]
So, the simplified expression is:
\[ \boxed{49 - 3\sqrt{5}}. \]