At what angle the hands of a clock are inclined at 15 minutes past 5 ?

At 15 minutes past 5, the minute hand is at 3 and hour hand slightly advanced from 5. Angle between their 3rd and 5th position.

 Angle through which hour hand shifts in 15 minutes is

${\left(15\times \frac{1}{2}\right)}^0=7{\frac{1}{2}}^{\circ }$

$\therefore$Required angle

$$\begin{gathered} =\left(60+7\frac{1}{2}\right) \\ =67\frac{1}{2} \end{gathered}$$