That's free to play, not free-to-play—an important distinction. Steam is again playing host to more (temporarily) free goodies, with a midweek trial of Civilization 5. The offer, which lets you play the full game until Thursday, 10am PDT, will give everyone a chance to experience the unstoppable wrath of Gandhi.
This, of course, is designed to prepare people for the upcoming Civilization: Beyond Earth, which has begun pre-loading ahead of this Friday's release. That game bears many similarities to Civ 5, only it's on an alien planet in the future. It is not, for instance, a game in which Genghis Khan can negotiate a beneficial spice deal with Bismarck.
Unfortunately, the free trial doesn't include the excellent expansions. Nevertheless, it's worth an investigation if, somehow, you've managed to hold off this long.