From the time on the clock, when will the two hands FIRST be exactly as far apart as the angle drawn beside it?

At 5:00 the minute hand is $150^{\circ }$ behind. It must close to $20^{\circ }$ behind, a gain of $130^{\circ }:\frac{130}{5.5}=23\frac{7}{11}$ min past $5.(30\frac{10}{11}$ is the later time, 20° ahead; $27\frac{3}{11}$ is when they overlap.)