At which player level are new gun levels unlocked?
Rank 5 unlocks at level 30.
Rank 6-10 unlocks every 10 levels past that.
If you go and try to research the weapons, you will see what the level requirements are for just about everything, the level requirements are standard across the board (this includes armor ranks).
The only piece of gear that seems to have no level requirements that I've found so far is the N7 chest piece.