$($a$)$ Use series to evaluate the limit

$\underset{x0}{lim}\frac{2sinx-ta{n}^{-1}x-x}{2x^5}$

$($b$)$ Evaluate the integral using infinite series.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{e^{5x}}{x^2}dx$