The engine's actual top speed was closer to warp 4.5 when Enterprise launched in 2150, although subsequent modifications improved this to a little over 5.1.
As of 2150, this was the fastest and most advanced engine used by Starfleet. It took Humanity almost one hundred years to develop their warp technology to this point. By 2160, Starfleet had developed a warp 7 engine. (ENT episode: "These Are the Voyages...")