Domain:
we know that a root cannot have negative values inside so
[tex]\begin{gathered} \sqrt[]{x}\ge0 \\ x\ge0^2^{} \\ x\ge0 \end{gathered}[/tex]the domain is X >= 0
Range:
we solve the equation for y
[tex]\begin{gathered} y=\sqrt[]{x}-5 \\ y+5=\sqrt[]{x} \\ (y+5)^2=x \end{gathered}[/tex]and we replace the condition that x must be greater than or equal to 0
so
[tex](y+5)^2\ge0[/tex]now solve y
[tex]\begin{gathered} y+5\ge0^2 \\ y+5\ge0 \\ y\ge-5 \end{gathered}[/tex]so the range is Y >= -5
then the right option is A
