Instead of playing 3 or 4 encounters in a session, try slowing each encounter down and playing 2 or 3, but having each one last longer. By slowing the pacing of the game down you may find that you can roleplay the situations you enjoy, and give everyone a part in the game, without running overtime. This does slow down your story development, so you will need to make adjustments. In my experience, this doesn’t feel much slower as a player, since you spend the time socializing and roleplay to the same degree.
One game I’m playing at the moment has gone that way due to the pacing change when moving from IRL to online. In a normal session, we get about 2 encounters done, down from about 6. Yes, less gets done per week, but in the end, it works and we still get to play. The campaign just takes a bit longer.
There are many ways to cut scenes short. Adding time pressure in-game, or out of the game can induce this easily.
During combat, you could introduce a turn timer. You have 10 seconds to state what you are going to do, or initiative moves on. This forces players to pay attention and make decisions when it isn’t their turn.
Out of combat, you can add time pressure by having an imminent event looming over the party which progresses at your discretion. For example, if the party has an audience with the king, have the king be impatient, introduce an aide who informs the king a more important guest is here. If they can’t figure things out fast enough, have the king end the scene. If the party is in a dungeon, roleplaying some camping, have thumping footsteps approach. Give the party something to react to, which develops when you want it to.
Whoever shows up, plays
Another solution I’ve used before is to allow a large number of players to join the game, knowing that it’s unlikely they will all be there every session. Yes, this may lead to you running 5 player sessions, but in my experience often someone can’t make it. If you make it clear to the group that it’s totally ok if they don’t show up, then halfhearted players won’t feel as pressures to show up (we all know what it’s like to have a long day, then jump into a game that you are honestly too tired to play, but you don’t want to let your mates down).
I had a particular PF group a long time ago where some players were pretty flakey. It was actually an 8 player game, but we ran with 4 or 5 most of the time. Often the monk spent weeks at local monasteries, and the dwarf spent many adventuring days sleeping off a drunken night.
Spending time with your friends is something you probably enjoy, whether you play or not. Likewise, just because your perfect game is suited to 4 players, maybe you can make some changes and play with 5. Ultimately you may not be able to come to a perfect solution, but playing your game with some changes to make it work with 5 may be worth it so you can play with your friends.
You may find that it’s worth sacrificing a little of the situations you like, and the roleplaying you prefer, so you can have everyone together hanging out.