Warp 3 engine cruise is Warp 2.2 or 73% top rated velocity. If that holds true for the Warp 5 engine it'll cruise at Warp 3.65.
Warp 5.2 for 12 hours is 0.19 ly
Warp 3.65 for 12 hours is 0.07 ly
Warp 3.65 for 18 hours is 0.10 ly
Warp 3.65 for 24 hours is 0.13 ly
Warp 4.8 for 12 hours is 0.15 ly
Warp 3.85 for 12 hours is 0.08 ly
Warp 3.85 for 18 hours is 0.12 ly
Warp 3.85 for 24 hours is 0.16 ly
Warp 5 for 12 hours is 0.17 ly
It appears that Warp 5 will be hit regardless of what we do, it's just a matter of time how long it is takes. Sprinting at Warp 5 for 12 hours and then "resting" at the higher (theoretical) cruise speed breaks even if the engines have to rest for 1.5×S where S is the time spent at maximum warp.
However when cruising the higher theoretical cruise is very impactful. 10ly cruising at Warp 3.65 would take 75 days, cruising at Warp 3.85 would take 64 days.
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Interesting aside; in ENT it's stated that Qo'noS is only 4 days away at Warp 4.5. Now if that seems absurdly close it's because it is. Using the Kirk warp scale that's only 1ly away, using the Picard warp scale that's only 1.64ly away.
Various sources place Qo'noS 90 to 112ly from earth. Traveling that distance in 4 days would require Warp 20-21 (Kirk Scale) or Warp 9.99 (Picard Scale). Using the Kirk Scale Warp 4.5 a 90 ly trip would take 360 days