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