Bow is a very underused weapon type in PVE. You get some bow builds here and there, but people don't utilize the weapon in end game very much. We used to use it, a while back, with the maelstrom bow, but that got nerfed a while back causing less and less people to even consider that backbar option.
The current change, a close range damage buff for all damage and a long range crit rate buff for all skills is great! It helps a lot! But 5% is a bit low, since you get more if you go with dual daggers and make one Nirnhoned. See, that's the strength of daggers. But with the crit rate buff, now we might consider doing a nirnhoned bow, since long range builds could make up for not using precise, the normal standard for 2-handed weapons, since you get two instances of crit rate from bow. The new buff is about a 6% increase in crit rate after all, so it basically makes up for the precise bonus on the weapon. But I don't think this will make it competitive.
My suggestion: Increase the close-range bonus of this new buff from 5% to 8%, and add another line to the Hawk Eye passive:
"Dealing damage with a Light or Heavy Attack increases the damage of your Bow abilities by 5% and your damage done to all enemies by 2% (or 3% maybe) for 5 seconds, stacking up to 5 times."