The answer is the first option, [tex]f\textsuperscript{-1}(x)=x^2+5; y \geq 5.[/tex]
When finding the inverse of a function, first replace [tex]f(x)[/tex] with [tex]y[/tex], and interchange the variables.
[tex]f(x)= \sqrt{x-5} \\
y= \sqrt{x-5} \\
x= \sqrt{y-5}[/tex]
Then, solve the equation for y. This will give you the inverse function.
[tex]x= \sqrt{y-5} \\ x^2 = y-5 \\ y = x^2+5 \\
f\textsuperscript{-1}(x)=x^2+5[/tex]
