After a repair, the two hands of this clock were fitted the wrong way round: the LONG hand now shows the hours and the SHORT hand shows the minutes. What is the actual time?

Treat the long hand as the hour hand: it is between 10 and 11, a little under halfway. The short hand, now the minute hand, is on 5, i.e. 25 minutes. The time is 10:25 (hour hand at $30\times 10+12.5=312.5^{\circ }$). Reading the hands normally gives about 5:52.