Answer
$\displaystyle \frac{x+4}{(x+5)^{3/2}}$
Work Step by Step
$\left[(x+5)^{-1/2}=(x+5)^{-\frac{3}{2}+1}=(x+5)(x+5)^{-3/2}\right]$
$(x+5)^{-1/2}-(x+5)^{-3/2}=(x+5)(x+5)^{-3/2}-(x+5)^{-3/2}$
... factor out $(x+5)^{-3/2}$
$=(x+5)^{-3/2}[(x+5)-1]$
$=(x+5)^{-3/2}(x+4) \qquad $... apply $a^{-n}=\displaystyle \frac{1}{a^{n}}$
$=\displaystyle \frac{x+4}{(x+5)^{3/2}}$
