In the expression \(5(g + 2) + 3(h - 4)\), the first property of operations that should be applied is the distributive property. This property will be used to distribute the 5 and 3 across the terms in the parentheses:
- For \(5(g + 2)\), apply the distributive property to get \(5g + 10\).
- For \(3(h - 4)\), apply the distributive property to get \(3h - 12\).
After applying the distributive property, you can then combine like terms if necessary.