Expand $\frac{e^{5z}}{(z-5)^3}$ around $z=5$
$$\frac{e^{5z}}{(z-5)^3}=\frac{e^{5z-25+25}}{(z-5)^3}=\frac{e^{25}e^{5(z-5)}}{(z-5)^3}=\frac{e^{25}\sum_{n=0}^{\infty}\frac{5^n}{n!}(z-5)^n}{(z-5)^3}={e^{25}\sum_{n=0}^{\infty}\frac{5^n}{n!}(z-5)^{n-3}}$$
Is it correct?