Or "simple impulse" is able to keep up with a Warp 5 Enterprise? Accelerating out to Warp 8 left the Romulan warbirds behind in "The Deadly Years". I'm assuming the reason why the Enterprise didn't initially just accelerate away was caused by the Commodore's inexperience. He waited too long by trying to contact the Romulans and the sustained weapons hits on the Enterprise forced the shields to use up energy that would've been available to accelerate out. Kirk's trick was to buy time for the emergency power to be built up for the acceleration to Warp 8.
Then again, they might have avoided a fight if they flew into the zone at Warp 8 in the first place
Contrast that with "The Enterprise Incident" where the Klingon warp engines was able to catch up with the Enterprise at Warp 9.