There are several games out there which give you the option — or even encourage you — to finish the game without killing a single other living being in the the virtual world. Usually RPGs like Deus Ex, boasting player freedom or stealth games like Thief or Dishonored are among those which offer this route. Some other games also facilitate pacifist runs.
GTA 5 isn't one of them. Or is it? A game that's all about crime, murder, power and money generally doesn't leave too much room for players to go all goody-two-shoes and spare the rod (gun?). The game hands you a weapon and boots you out into a rough and dangerous world.
Countless missions specifically have an objective of killing someone or even multiple someones. Other objectives cannot be completed without killing multiple someones. Even if neither of these are true, it is generally really really hard to complete any mission objective without taking a life.