That is Right.
+5 means he has a 20 or 21 in dex. Getting to 20 by level 6 is hard (considering that they've only got one ASI), but possible using rolling for stats. The +2 and +3 are correct, and you allowed the +1 bow (which isn't unreasonable).
When not rolling for stats, the standard array max is 15 + 2 from race + 2 from ASI, i.e. 19 ― a +4 instead of a +5.
Remember, these are epic characters who fight, and shoot, a lot -- it is their job in life. Hitting 80% against AC 16 makes sense by level 6. The damage from even a longbow is only 1d8 + 5 (+1 from magic weapon above?) which isn't a spectacular DPR when you multiply it out. I mean, it isn't bad, but it isn't as high as some other classes. Moreover, certain classes peak at different levels. Even taking Hunter's Mark into account, it compares pretty well with the other classes' DPR.
Consider the other classes at the same level:
The fighter has fighting style, extra attack and action surge by then.
The barbarian has +2 rage damage, reckless attack and extra attack.
The Paladin has smites, fighting styles, and extra attack.
The Warlock can be doing 2 EB blasts each doing (spell attack 1d20 + 4) at 1d10 + 4 (+ 1d6 hex), pushing 10ft from 300ft away by then.
Your DPR Might be too High from Homebrew
Adding another 1d6 or 1d8 to an attack on top of Hunter's Mark will almost certainly unbalance a game, unless the whole party has extra buffs beyond stock +1 weapons.