Divide throughout by x:

MATH

Here, $P(x)=-\dfrac{4}{x}$ and $Q(x)=x^{5}e^{x}$

IF MATH

Now MATH

Applying the formula: MATH gives

$dx+K$

This requires integration by parts, with

MATH

MATH

So

$\qquad y$ $x^{-4}$ MATH

Multiplying throughout by x4 gives:

MATH