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Warp 5? That's really slow.
I'd say their common travel speed is more like warp 7.
Guess it's time for another entire rewatch of TNG to check the stats.
Warp 8 was the most common warp factor used for general travel on TNG. Warp 9.2 was actually the maximum sustainable cruising speed of a Galaxy class ship. This was played for a laugh in Menage a Troi when Picard called for Warp 9 when returning Lwaxana to Betazed at the end of the episode.
Near the end of the series didn't they set a speed limit of warp 7?
In Force of Nature (S07E09) they discover that high speed warp travel can damage the fabric of space and a speed limit of warp 5 is set by the Federation for non-emergency travel. It gets referenced a couple of times in the final season of TNG but doesn't come up much after.
Though arguably Voyager's situation and the Dominion War could both be reasonably considered "emergencies". It's also been suggested that the Federation was very quick to develop warp drives that didn't cause this damage (this is one official but never-published explanation given for the Intrepid Class variable geometry warp nacelles).