Q:

Balance of Longbows (+ammunition) vs. 2h Melee Weapons

This question has 2 parts, but any information that provides context to help me understand how these weapons compare is appreciated.
Primary Question: Would it be considered "balanced" to award a player with a +2 Longbow, instead of a +2 Greataxe?
Secondary: How does the possibility of magical ammunition play in to this decision?
Context
I am running a published campaign and the final encounter of this "chapter" provides a +2 Greataxe. All the characters are finesse-based (or a Moon Druid) and thus I was hoping to change this out for a Longbow for our ranger. 
All the other characters have received magic items by this point except the ranger. The ranger does, however, have three +1 arrows. I am concerned that the +2 Longbow might be stronger than intended for the character level (5), and the magical ammunition compounds that, even though it would only provide a temporary boon. Campaign wise he will not receive any additional magic ammunition until level 13 or so, and it too will be of limited quantity.
Does the range bonus, and ability to shoot magic ammunition, make this longbow considerably more powerful than the Greataxe it replaces? If so, should this be mitigated by allowing a +1 Longbow instead, or requiring a gold component for "trading" in the Greataxe for a Longbow?
Lore-wise for this chapter of the campaign there is a reason (although its not really story progression relevant) for the actual treasure to be an axe. The character would trade this axe into a collector (it contains a specific master craftsmen's insignia) and would receive a +2 Longbow as a reward. This would be a minor role-play element in-between adventures. 

A:

I don't see any issue with it.
The range situation doesn't change anything as far as swapping weapons out.  A +2 attack and damage bonus is just that, regardless of how the weapon is used.  Rarity is based on the bonus, not on the weapon type.
Stacking magical ammo isn't a big concern since it's effectively one shot only.  Three times, the player can hit very slightly harder and very slightly more accurately.  It's not a big deal.  I've always considered that the point of magical ammo is primarily to give an archer with a mundane bow a way to punch through "non-magic weapon" resistance.  Since arrows fired from a magic bow can do that automatically, the impact of hitting slightly better three times is minimal.
As to level, I don't think that's a real concern. A +2 weapon is definitely strong for a level 5 group, but it's not unbalancing.  There's no need in 5e to keep up with the magical joneses, so your ranger may well use that single bow for the rest of his entire career. (Because of this, you might want to put in some extra effort to make the bow really neat -- give it a special name and design, or something, don't just say 'And you find a magic +2 bow!')

