$\lim \limits _{x \to \infty} \bigg(\large\frac{x+5}{x+2}\bigg)^{x+3}=$

Question

$$\begin {array} {1 1} (1)\;e & \quad (2)\;e^2 \\ (3)\;e^3 & \quad (4)\;e^5 \end {array}$$