This should be a great combo.
Not necessarily, as I see it.
According to the impedance curve shown
here for the Cornwall II, its impedance is in the vicinity of 5 ohms at most bass and mid-bass frequencies, while rising to much higher values at most higher frequencies.
Learsfool (whose sonic perceptions are always above reproach IMO) mentioned that he obtains excellent results using a Dialogue Two with Cornwall IIs. However your Five is described as using zero feedback, with its description pretty clearly implying that the Two, from which a lot of its design is derived, used significant amounts of feedback. Which presumably means that the unspecified damping factor of the Five is significantly lower than that of the Two, and its output impedance (which is inversely proportional to damping factor) is therefore significantly higher than that of the Two. Typically a zero feedback tube amp will have an output impedance that is a significant fraction of the five ohm impedance your speakers have at most lower frequencies, which will result in an under-emphasis of those frequencies relative to frequencies at which the speaker impedance is much higher. Which in this case would mean an over-emphasis of most frequencies in the mid-range and lower to mid-treble regions, relative to the bass and mid-bass regions. All of that being in contrast to the frequency response that would result with the near zero output impedance and very high damping factors of nearly all solid state amps.
So while several good points and questions have been made and asked, including those regarding trying the 4 ohm taps, checking speaker phasing, and the possibility of weak tubes, it seems to me that the damping factor and output impedance characteristics of the particular amp may simply not be a good match for how the impedance of the speaker varies as a function of frequency.
Good luck. Regards,
-- Al