\displaystyle \lim_{x \to e} \left(\frac{2^{\ln{x}}+3^{\ln{x}}}{5}\right)^{\frac{1}{\ln{x}-1}}=e^{\displaystyle\lim_{x \to e} \frac{2^{\ln{x}}-2+3^{\ln{x}}-3}{5(\ln{x}-1)}}=\ldots=