The current time is between 1 o'clock and 12 o'clock in a wall clock and both the minute hand and the hour hand are situated precisely on two distinct minute marks.

It is observed that the hour hand is precisely a pentagonal number of minute marks ahead of the 12 hour mark. The number of minute marks by which the hour hand is ahead of the minute hand is also a pentagonal number greater than 1.

Determine the current time from the information provided in the above statements.