\(\sqrt{5+x}\) is defined as long as \(5+x\ge0\), or \(x\ge-5\). However, \(\dfrac1x\) is undefined when \(x=0\). This point is contained in the set \(\{x|x\ge-5\}\), so we need to exclude it. We can write the domain in several ways.
\(\{x|x\ge-5~\land~x
eq0\}\)
\(-5\le x<0~\land~0
\([-5,0)\cup(0,\infty)\)
