Answer
$$Convergent, \frac{e^{-10}}{5}$$
Work Step by Step
$$\int_{2}^{\infty }e^{-5p}dp=\lim_{t\rightarrow \infty}\int_{2}^{t}e^{-5p}dp$$
$$=\lim_{t\rightarrow \infty} \left| -\frac{e^{-5p}}{5} \right |_{2}^{t}$$
$$= \lim_{t\rightarrow \infty} \frac{-e^{-5t}+e^{-10}}{5}$$
$$= \frac{e^{-10}}{5}$$
Convergent