The pursuit of Enterprise NX-01 by corrupt Mazarite officials trying to kill the Vulcan ambassador V'Lar before she could give evidence against them, during which the ship first reached warp five.
In the Enterprise episode Fallen Hero, the Vulcan High Command asks Archer to collect Ambassador V'Lar from Mazar, where she has apparently been expelled in disgrace, and carry her to the Vulcan ship Sh'Raan. T'Pol, who has admired V'Lar since childhood, is dismayed by the charges.
Mazarite ships soon demand that V'Lar be handed back and open fire when refused. V'Lar at last admits that the scandal was staged to get her out safely: she holds evidence against criminals who have infiltrated the Mazarite government, and they want her dead.
Archer runs for the rendezvous, driving the engines to warp five for the first time. When the Mazarites board, he lets them believe V'Lar is in a sickbay chamber that they then shoot up. The Sh'Raan arrives, and V'Lar walks out alive.