Here is my party breakdown. We would be pretty good at combat, except that we don't focus fire very well (the times that we do, we are very effective).
Warlock (me). I use hex (I'll come back to this later) and eldritch blast to dish out a solid ~9 DPR. My pseudodragon also works for putting enemies to sleep. My opener is usually a nice shatter (on which I've never rolled lower than 16 damage and enemies usually fail their saves) when most of the enemies are clustered together. I would be mostly a controller with hex (I'll get back to this, as I said) and sometimes suggestion (when there isn't a good shatter situation).
Paladin. The paladin is the low-damage defender you guys talked about. He's not exactly low-damage, except he never hits with anything except opportunity attacks (but when he does hit, it's usually a crit and he can smite for MASSIVE damage). He has high Con, Heavy Armor Master feat, AC 21, Sentinel feat (he's never missed an opportunity attack), Protection Fighting Style, and Compelled duel. He keeps the enemies attacking him and away from the rest of us squishy casters. Now for my hex, I often do Strength, so the paladin can shove enemies out the door and hold it shut if things get tough.
Rogue. The rogue does a lot of sneak attack, but usually misses. He is very helpful outside of combat though, because he always rolls 13 or higher on Stealth checks (+7 modifier, for at least 20). He sneaks in places and scouts it out, usually accompanied by my pseudodragon.
Cleric. This ain't your normal cleric. He is trickery domain and has almost no healing capabilities. Instead, he uses inflict wounds and spiritual weapon for INSANE DPR, while using his channel divinity (illusory duplicate) to keep his enemies from hitting him. This guy is definitely our striker.
Gnome. This guy has a table that he DMs, so he only plays with us occasionally. He is a gnome champion fighter with plate mail (another AC 20 guy) and protection fighting style. He is another nice tank, and he and the paladin just stand in the way and can't get hit, and the enemies can't get to the rest of us. He rarely ever hits, but when he does it's usually a crit. Another defender, definitely.
In 5e, I would say that there definitely are roles, but they are not nearly as essential as in 4e. Also, in 5e roles are based more on build than class. The paladin could have easily taken Oath of Vengeance and dueling style and dished out a ton of damage, and my warlock could just have easily taken fiend pact, armor of agathys, and fiendish vigor and always have a bunch of temporary hit points. The gnome could have taken battle master and pushed people around and disarmed them and stuff. I noticed that our group works very well in combat, with the paladin standing in the way and using compelled duel on any stragglers, while we three just sit 40 feet away and shoot. That's not exactly defender/controller/leader/striker, but it's close enough: defender/striker/controller/rogue who doesn't help much. I've noticed with that balance, we can be very effective in combat, assuming we focus fire (in our last encounter, we had to run away from a few duergar, who after we ran away, the DM told us were at 2, 5, and 7 hit points; if we had taken them out one at a time, we would have won).