The opposite of x squared plus 5 is -x² - 5.
The inverse of an expression f(x) is another expression f⁻¹(x) that "undoes" what f(x) does. In other words, f⁻¹(f(x)) = x for any value of x in the domain of f(x).
The additive inverse of an expression f(x) is another expression -f(x) that, when added to f(x), results in 0. In other words, f(x) + (-f(x)) = 0 for any value of x where both expressions are defined.
In your question, we're dealing with the additive inverse. The expression "x squared plus 5" can be written as f(x) = x² + 5. Therefore, its opposite, as an additive inverse, is -f(x) = -x² - 5.