Hmmm, I'm running Service Pack 2, and I ran the DXSetup.exe file to make sure I actually have the most recent version of DirectX, but the launcher still says "update required" for the DX10/11 option.
Such a problem frequently appears if a person is under Win7, and Steam and/or Civ5 are in Vista compatibility mode. That does not apply to you, for sure.
But...maybe...could you check if Steam and Civ5 are maybe in another form of compatibility mode?
(how to check: right click on the .exe file -> properties -> tab for compatibility mode)
Every time I use Dx11 option, the game crashes within 5 minutes. Every time. I got sick of it and have had no crashes with 9.
Oh...uhm...
DxDiag please?
And have you already updated the graphics card drivers?