A limit of warp five placed on Federation ships after scientists proved that warp fields were damaging the fabric of space in heavily travelled regions.
The warp speed limit is a rule issued by the Federation Council in 2370. It holds all Federation vessels to warp five except in an emergency, in order to slow the harm that repeated warp travel does to subspace.
It comes about in Force of Nature. In the Hekaras Corridor, the only safe route through a region of intense radiation, the Hekaran scientists Rabal and Serova disable passing ships to draw attention to their theory that warp fields are wearing space away. When the Enterprise crew still doubt it, Serova blows up her own ship's warp core and opens a rift, proving her case at the cost of her life.
The limit is mentioned in several later episodes, usually when a ship is given leave to exceed it, as happens in The Pegasus. Later starship designs appear to have overcome the problem.