That sounds like a lot of work. Being a Steam game, the ability to take screenshots is built right in. No tabbing out, opening other programs, etc. Just a keystroke, and it goes into a screenshot folder for that game.
The screenshot key in Steam is F12.
You need to change it something else (I use ctrl-F12), since Civ5 uses F12 to quickload, then you're all set to take screenshots all day long.
To change the keybind, in the Steam client go to View > Settings > In-Game.