Gad damn Civ V is addicting. I started a game as the germans, its been a while since I have played but I quickly dominated the surrounding areas. Kinda bloomed late, fought the Indians in the medieval era, but wasn't ready for conquest so accepted their peace offer. In the Renaissance I conquered the Indians, then slowly took some territory off the Songhai. Once I hit the late industrial era I decided to go nuts. Conquered America (the other civ on my continent, and finished off the Songhai, who have expanded into the islands in the ocean (making for good air and naval bases).
The other continent is dominated by the egyptians, a smaller but more technologically advanced empire (they're already in the future era, which is worrying for me), reasonably powerful greeks, a tiny Japanese state and what used to be the iriquois, conquered by the greeks. I'm preparing for a fullscale invasion but I don't think I will have time left to completely conquer the other people.
Out of curiosity what are the various victory conditions for Civ V?
Depends if you have Brave new World installed.
There's domination where you're the last player still in control of your original capital.
There's the science victory where you build and launch the spaceship.
There's the cultural victory where:
Without Brave new world you just fill up three policy trees and then build the Utopia Project.
With Brave new world you have to boost your Tourism rate ("aggressive" culture) to supplant other civ's cultures. Once you do that you win.
There's the diplomatic victory:
Win a vote in the United Nations. Without brave new world it is a buildable wonder, someone has to build it for the elections to start. With Brave new world there are automatic conditions for it to be formed: either one civ gets to the information era, or more than half get to the atomic era.
EDIT: oh yeah, there's the score victory too. Civ with the highest score at the end of the game's time period wins.
In your case you "might" be screwed, as there's a civ already in the future era. They might be already building spaceship parts. Though IIRC, you get a warning once a civ's built the Apollo Project.
You should also check if they have already built the Manhattan Project.