Seems like a simple thing, but it got my whole group in an argument. It was over the Assassin level 3 encounter power "inescapable Shadow" which states Before the attack, teleport 5 squares to a square adjacent to the target of one of your assassin shrouds. I interpreted this as meaning that despite it being a melee attack, you could teleport five squares if you weren't adjacent to a target in the first place to reach an escaping opponent. One of the other players thinks that as it is a Melee attack, that you have to already be adjacent to the target and can then only use the teleport to get behind them or next to them. I need this argument to be over before my next session, please help.
You are correct.
The "melee" restriction applies to the attack line, not the effect line. When you make the attack, your target must be in melee range or the attack fails. It does not need to be in melee range when you teleport.
The range could apply to the effect line if the effect line explicitly says it does. Consider, for example, the wizard at-will power Storm Pillar from Arcane Power. Its range is Ranged 10, and its effect begins with (emphasis mine): "You conjure a pillar of crackling energy in an unoccupied square within range..."
To look at this from another perspective, consider the wizard 1st-level encounter power Grasping Shadows, also from Arcane Power. Its range is Area Burst 1 within 10 and it targets each creature in the burst. It also has an effect line creating a zone in the burst. It would be entirely legal to use this power to target an area that currently contains no creatures; it would still create its zone, and that zone would still have its effect on creatures that entered the zone. The attack uses the range to determine valid targets when the attack is made; the effect line does not use the range unless it explicitly says so.
On a final note, the Dragon magazine assassin is such a painfully bad class that it can be worth ruling in its favor even when the rules don't support it (though in this case they do).