But Warp 5 is effectively the speed limit within a Solar System,
presumably due to the increased levels of interstellar(planetary)
dust present, so this could be a realistic reasoning for the change
in formula after warp 5.

According to the calculated values, warp 1 is the speed of light,
warp 4.8 is 111 times the speed of light, warp 5.4 is 850 times
lightspeed and warp 8 is 4096 times lightspeed. This allows for
the Romulan Neutral Zone to be situated in the Beta Quadrant between
c.350 and 1700 light years from Sol in the direction of the Delta
Quadrant*. This also allows for the Romulans to have a vast empire,
most of which is in the Beta Quadrant of the Galaxy, thus explaining
why most of the Federation/Federation exploration is in the Alpha
Quadrant.

http://memory-alpha.org/en/wiki/Alpha_Quadrant
http://memory-alpha.org/en/wiki/Beta_Quadrant
http://memory-alpha.org/en/wiki/Gamma_Quadrant
http://memory-alpha.org/en/wiki/Delta_Quadrant

Apparent disparities: Obviously being a television
and film series not everything in Star Trek should be considered
canon (i.e. the changing appearance of the Klingons and Trills,
the postponement of World War Three), but there are some apparent
glaring contradictions with the limits on warp speed. For example,
in “The Final Frontier” both the Enterprise and a Klingon Bird
of Prey travel from a system in the Klingon Neutral Zone. to the
apparent centre of the Galaxy in a manner of days-presumably a
distance of at least 20,000 light years-when it would normally
take probably six years for a starship to traverse such a distance
(a very conservative estimate)**. However, for the purposes of
making a fast-paced filmed drama it would hardly do for long scenes
of the Enterprise crew playing cards or reading “War and Peace” for
the tenth time! A six-year journey would, however, fit in nicely
with the timescale for significant Federation events given in:

http://memory-alpha.org/en/wiki/Federation_history - Summary_of_key_dates

Which states the events in the Kirk movies taking place over a
nineteen year period (up to “The Undiscovered Country”), while in
the real world they were in production over a twelve year period.
This may also explain why the, apparently newly-constructed,
Enterprise-A was ordered to be decommissioned at the end of
“The Undiscovered Country”.

[• 2272: An attack on Earth by a massive machine lifeform called
V'Ger is closely averted. ***
• 2286: Another devastation of Earth is averted, when a reply to a
probe of unknown origin can be given, whose attempts to contact
Humpback whales severly affect Earth's atmosphere.
• 2293: On the Khitomer Conference between the Klingons and the
Federation the Khitomer Accords are
signed to establish a lasting peace between the two powers.]

*In the NG episode “The Neutral Zone”, the Enterprise crew discover
and revive three cryonically preserved humans, who ‘died’ in the
late 20th century, near the Romulan Neutral Zone. Presumably the
pod/ satellite containing them was accidentally taken in by the warp
wake of one or other of the ships establishing one of the Earth
colonies which (TOS) had been established near what would become
the buffer zone between the Federation and the Romulan Star Empire
at some unspecified time in the 22nd century when traveling these
distances had become feasible for Earth-built starships.

No real details of the RNZ are described, but it is reasonable to
assume it extends at least 1500 light years in a roughly straight
direction between the RSE and the UFP facing roughly ‘north’ in
the Galactic plane towards the Delta Quadrant as this distance is
the thickness of the Galaxy/ Galactic plane (think of the Galaxy
as a dish 1500 light years thick on average) in order to allow no
opportunity for it to be circumvented by one side or the other .

http://memory-alpha.org/en/wiki/Romulan_Neutral_Zone

**When Q transports the Enterprise-D 7000 l.y into the Delta
Quadrant, Data comments that it would take two years to reach
the nearest Starbase.

***If this date is canon, the events take place three years at
most after Kirk’s five year tour of duty, but “Star Trek: The
Motion Picture” was in production ten years after the Original
Series was made.