To rephrase, the statement of the problem says

"A clock gains 300 seconds every 3600 seconds; find the angle that the second hand traverses in one minute."

So the clock says 3900 seconds have passed every 3600 seconds.

Then, 65 seconds pass on the clock every 60 seconds.

Then, 65 seconds pass on the clock every minute.

The question is now, how many degrees will the second hand traverse after 65 seconds pass on the clock? Every 5 seconds on the clock, we see that the second hand traverses 30°. So in 65 seconds on the clock, it has traversed 390°. The answer is 390°.

Did my solution make sense?