This is just a photoshopped image as an example, right? In the actual episode, Pressman wore two boxed pips throughout.
That's true, Quinn's uniform didn't though. TNG s1 & s2 showed us 'no pip', 'one pip' and 'two pip', TNG s3 onwards showed 'two pip', 'three pip'* and 'four pip'. No five pip has been seen on that system or any system in the Prime Timeline.
I think it would be unlikely that any flag rank would have no insignia at all. I would tend to believe that system used 1 to 5 boxed pips, rather than 0 to 4. YMMV.
The only potential evidence for a 'five star' insignia of any sort being used in Star Trek (based on onscreeen evidence) at all is in the Abramsverse, Alexander Marcus, the Head of Starfleet (equivalent of at least one of the Joint Chiefs if not the Chairman, possibly with elements of SecNav or SecDef) wore 'five lozenges' on his dress uniform, compared to Pike's four (who wore three stripes on his working uniform), and given that VADMs hold many of the roles that ADMs/GEN do in the US Forces then it seems unlikely that they would need a higher rank than that. A possible scheme (based on TOS or naval ranks) would be:
Broad stripe (one star in UESF) = Commodore (referenced in text during Conspiracy so the implication that this in an Admiral rank is likely erroneous).
Broad stripe + medium stripe (two-star in UESF) = Rear Admiral.
Broad stripe + 2 medium stripes (three-star in UESF) = Vice Admiral.
Broad stripe + 3 medium stripes (four-star in UESF) = Fleet Vice Admiral (based on the French rank of Vice-amiral d'escadre [Squadron Vice-Admiral]).
Broad stripe + 4 medium stripes (five-star in UESF) = Fleet Admiral.