Question

for which values of x does each expression make sense? the square root of x+5

Answer 1

You have the following expression:

$\sqrt[]{x+5}$

take into account that you can apply the square root only for numbers greater or equal to zero.

Then, it is necessary that:

$\begin{gathered} x+5\ge0 \\ x\ge-5 \end{gathered}$

Hence, for values of greater or equal to -5 the square root makes sense.