I don't think so. If your league finishes in the top two in the yearly rankings you have to get an "extra" Champions League place. If the team finishing fifth wins Champions League/Europa League then the league would ordinarily have five places, so to ensure that they get an extra place, sixth spot qualifies, too.
Theoretically, seventh could qualify, though that wouldn't benefit us as it would only happen if we had qualified anyway by winning the Europa, and finished 5th/6th while Liverpool took the other 5th/6th spot and won the Champions League.