How do you evaluate a limit
Alternatively, $\displaystyle \frac{5x-1}{5x+3} = \frac{5x+3-4}{5x+3} = 1 - \frac{4}{5x+3}$
And use the fact that $\displaystyle t^{5x+2} = t^{5x+3-1} = t^{5x+3} \cdot t^{-1}$ and that $\displaystyle \left(1 + \frac{a}{f(x)}\right)^{f(x)} \rightarrow e^a$ as x goes to infinity and f(x) goes to infinity.