In Star Trek: Enterprise, the NX-01 was designed to achieve warp 5.
The NX-01 is Earth’s first warp-five starship and the first human vessel intended for sustained deep-space exploration at that speed. Its propulsion system represents a major advance over the earlier NX-class prototype ships, allowing Captain Jonathan Archer’s crew to travel far beyond the limits of previous human missions.
The ship’s launch follows the development of the warp-five engine by the United Earth Space Probe Agency, with significant work associated with Henry Archer. The Enterprise begins its mission in 2151 and becomes the first human starship to explore many regions later connected with the Federation.
Warp 5 is a design goal and technological milestone, not the same as the ship’s speed on every mission. In Star Trek, warp factors describe faster-than-light travel, but a starship may use different speeds depending on safety, engine limits, and mission conditions.