Find the limit $(\frac{n}{n+5})^n$ 
Find the limit -$$\left(\frac{n}{n+5}\right)^n$$

I set it up all the way to $\dfrac{\left(\dfrac{n+5}{n}\right)}{-\dfrac{1}{n^2}}$ but now I am stuck and do not know what to do.

$$\mathrm L=\lim_{n \to \infty}\left(\frac{n}{n+5}\right)^n \implies \ln {\mathrm L}=\lim_{n \to \infty} n \underbrace{\left(\frac{\ln \left( 1-\frac{5}{n+5} \right)}{\frac{-5}{n+5}} \right)}_{\text{This limit is 1}} \times \frac{-5}{n+5}$$$$ \implies \ln{\mathrm L}=\lim_{n \to \infty}n \cdot \left(\frac{-5}{n+5}\right)=-5$$
$$\implies \mathrm L=e^{-5}$$
