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Duration always advances on the upkeep phase of the permanent controller of a card with a duration. In your scenario, the first tick will happen on your opponent's next upkeep phase and will complete on his fifth.
On a related note, does discard phase of turn 1 to draw phase of turn 2 count as 1 turn for cards such as Pentecost, Passover & Unleavened Bread, etc? Like you can just set your heroes aside at the end of your turn during discard phase and then on your next turn get them back during upkeep and gain the benefit?
That is correct. Turns are counted on your upkeep. It doesn't matter when the card gets set-aside. Other examples of "quick turns" are Pretention on your Hero during your opponents discard phase. Or the "shame" Lost Soul sets aside Heroes during your draw phase (next is upkeep so it's 1 turn already for your Hero).
There are 2 common ways to keep track of turn counts (whether set aside or turns-in-play, such as Seven Years of Plenty):1. Putting a die with a face value, or a number of counters, equal to how many turns the character will be set aside. When the die would be turned to 0, or you remove the last counter, the set aside effect is done.2. Using a die, or a number of counters, to count up the number of turns that have passed. In this case you wouldn't put the die or any counters on the card until the first time it "ticks" which would be the controller's next upkeep phase. When the die, or counters, equal the set aside's duration the set aside effect ends.In both cases, nothing "ticks" until the card's controller's first Upkeep Phase after the set aside ability is activated. Hopefully that makes sense.