If the minute hand "ticks" into place every minute then:
Every hour the hour hand moves 30 degrees, so every minute it moves 1/2 a degree. As there are 60 minutes in an hour, each minute that passes corresponds to 6 degrees (6*60=360). So, at 1:05 the minute hand will be at 30 degrees while the hour hand is at 32.5 degrees, and at 1:06 the minute hand will be at 36 degrees and the hour hand at 33 degrees. So it passes as it goes from 1:05 to 1:06 (during the "tick"
If the minute hand moves smoothly throughout the minute (rather than simply "ticking" into place the moment a minute has passed).
Then, every second that passes corresponds to 1/60 of 6 degrees for the minute hand (1/10 degree) and every second that passes corresponds to 1/60 of 1/2 degree (or 1/120 degree). At 1:05 M=30, H=32.5. So to figure out how many seconds, solve for x:
30+(x/10) = 32.5 +(x/120)
(27.2727 * 1/10)+30=32.727272 degrees for the minute hand
(27.2727 * 1/120)+32.5=32.727272 degrees for the hour hand.