That was quick, as we knew it would be. Mods have begun to appear for Grand Theft Auto 5 (check out our review in progress here), and this mod posted over on Reddit by DrDaxxy allows you to set a custom field of view for first-person mode. The vanilla game's FOV is fairly constrictive, so it's not much of a shock that modders immediately started working on a fix.
This mod only takes effect when walking in first-person mode—first-person driving, or playing in third-person mode, are not changed. However, it does work in GTA 5 Online as well as single-player story mode, and works for both the Steam and Rockstar Warehouse versions of the game. You can take a look at some comparison shots here.
WARNING! At the moment, it's not clear if this mod could get you banned for cheating. Since the mod works in GTA 5 Online, and changes the memory settings, it could be viewed as a figurative cheat and possibly result in a ban. Frankly, it could also be seen as a literal cheat, since you'll have a more expansive view than other players. Use this mod at your own risk! Better yet, let someone else use it at their own risk and wait to see if anything bad happens to them.
You can read all about it in the modder's post on Reddit, including instructions on how to get it running. There's also video of it being used with the FOV set at 110 here.