What is the maximum warp speed in the Original series?

I've watched the Original Star Trek series and the newer Enterprise series, but have never been able to figure out something. Enterprise is about the first Warp-5 ship, but I've been told that the original series ship couldn't reach Warp-5 without pushing
warp six
daniel | Jan 21, 2010
A few billionths of a second early? 10x speed of light is what we need "captain kirk more power to the warp engines"