The parent function is
[tex]g(x)=x^2[/tex]
This function was transformed to obtain h(x), the transformation applied is represented by the following expression:
[tex]h(x)=g(x)-5[/tex]
When you add/subtract a constant "k" from a function the type of transformation is a vertical translation.
For example, considering any function f(x)
-If you add "k" units to the function: f(x)+k, the resulting transformation will be a translation of "k" units up.
-If you subtract "k" units to the function: f(x)-k, the resulting transformation will be a translation of "k" units down.
With this in consideration, there were 5 units subtracted from g(x), which indicates that the function was shifted vertically 5 units down.
The correct option is B.