There was never really a big 5 in the 80s though IMO. From what I can deduce, that was a PR campaign bought and paid for by those very clubs. The original plan set in the late 80s, was obviously to create are legitimate big 5 in the PL era. Then it quickly became a big 3, when it eventually arrived. Spurs were a mid table club at best for the first decade and half of the PL era. Everton faired slightly better without really challenging much(how many title challenges, how many trophies in the PL era?).
It was a big two at best going into the PL era, Liverpool for the success(miles clear of everyone in major honours with 32 by the end of the 80s), United(15 m-h) for their attendances(have to give them that unfortunately).
Arsenal(16 m-h), Everton(14 m-h) and Spurs(14 m-h) had no legitimate claims to put themselves above the other traditional top clubs of old english football. There were too many clubs, too close to them to claim they were bigger. Wasn't there only 1 televised game a week for most of that era(Liverpool taking most of the limelight)?