What was the fastest a Vulcan ship could go during the 22nd century, since the enterprise could only go as fast as warp 5
The Suurok-Class vessel Sh'Ran is noted to be able of reaching warp 7. Given that it's a relatively new vessel and intended for combat, I think it's reasonable to assume that it represents the cutting edge as far as engine design is concerned.
ARCHER: What if we could get a message through? Tell them to get here as fast as they can.
T'POL: The Sh'Raan is capable of warp seven. If we could maintain warp five we'd reach them in twelve minutes.
Historically, we've seen ships exceed their stated max-warp parameters by around 5-10%, suggesting that the Sh'Ran's absolute tippy-top speed is around warp 7.5 before it shakes itself apart.