\( \Large \frac{p}{q} + \frac{q}{p} = \frac{p^{2} + q^{2}}{pq} \)

\( \Large = \frac{ \left(p + q\right)^{2} - 2pq }{pq} = \frac{ \left(10\right)^{2} - 2 \times 5 }{5} \)

\( \Large = \frac{100 - 10}{5} = \frac{90}{5} = 18 \)