Here is the original problem

$\displaystyle

$$\displaystyle \lim_{x\to-1^-}\frac {5} {(x+1)^3}= \infty

$

So you do

$\displaystyle \frac {5} {(x+3)}<N$ whenever $\displaystyle -1-\delta <x<-1$

Then you need to solve for x+1 to move on to the next step, but I don't know how...

The book says you should get $\displaystyle \sqrt [3] {5/|N|}$... but I can't figure out how to get the absolute value.