As I had such a great response to my last question, I'd like to check my workings are correct for this one. I have:
$\left|\frac{1}{(m+5)^3} - \frac{1}{(n+5)^3}\right|<\epsilon$
LHS $\leq \left|\frac{1}{(m+5)^3}\right| + \left|\frac{1}{(n+5)^3}\right| < \left|\frac{1}{m^3}\right| + \left|\frac{1}{n^3}\right| \leq \left|\frac{1}{n_{0}^3}\right| + \left|\frac{1}{n_{0}^3}\right| < \epsilon$
Therefore, $\epsilon > \frac{2}{n_{0}^3}$
Which leads to $n_{0} > \sqrt[3]{\frac{2}{\epsilon}}$
All comments appreciated. Thanks.