The given expression is
[tex]h(x) = \frac{5}{\sqrt{2x+10}}[/tex]
THe given expression is a rational expression, and rational expression should not have 0 in the denominator.
Moreover, the denominator is a square root term, and square root don't have a value for negative number .
Therefore 2x+10 must be greater then 0. That is
[tex]2x+10>0 \\ 2x>-10 \\ x>-5[/tex]
Therefore the required domain in set builder form is
{[tex]x | x>-5[/tex]}