Tick sound on every pedal only for 5 minutes
Possible cause:

Without any further knowledge about your bike, I'd guess that the clicking noise has something to make with a grease in either the pedal or the crank bearings. (As you mentioned that the sound occurs only when the pedals are in the very same position and when you actually put some force on them, I'd say it isn't caused by something like an unevenly tightend handle bar or loose seat post etc etc..)

Since you only hear the clicks within the first 5 - 10 min when riding, I assume this is the time the grease needs to "warm up", as in become slightly more fluid due to the friction it experiences. During this time some of the little balls inside the bearings could cause the clicking noises.

Possible solution:


Make sure that the pedal bearings arent tightend too much (in case
you can open them at all).
check on your cranks, whether they're tightend properly
check on the more unlikely sources for the click (i.e. seat post, saddle, etc.)
replace bottom bracket


I'd also advice you to do these steps iteratively, so you get to know the source of the problem.