I've run for as many as 12 players - in 4e, no less - and it's doable. In 5e, I haven't had that many, yet, but have still bumped up against the per-table limit. In 5e, table & party composition really matters. Some players can take their turn quickly and stay engaged while it's not their turn, some (OK, a lot) lose focus and you have to refresh the T of their M at the start of their turn.
Combat may slow down when you have many players, but if you budget time & challenges accordingly - have fewer, more difficult combats in a session - it's manageable in aggregate. Combat is also the easiest pillar to keep all your players involved, because of cyclical initiative, everybody gets a turn. Ideally, they stay engaged when it's not their turn, and enjoy the whole game, not just the 1/7th of it when they're declaring actions & rolling dice. Ideally. ;( But, at least, everyone participates in every fight.
It's the other two pillars that can be problematic. The social pillar tends to be dominated by the players (not PCs) with the more assertive personalities. Y'know the drill, you introduce an NPC and one or two players perk up and start talking in character - and 5 phones come out. The exploration pillar borders on netrunner syndrome, with the specialist in the current environment tending to eat up play time - others just have nothing much to do, unless you salt the environment with bits of their specialties.
One thing you can do in both cases it to adapt what works in combat - turns. Go around the table and get what everyone is doing before letting the forceful social types or exploration experts take the next step. It won't eliminate the problem, but it will have a shot at keeping everyone more engaged.