Optimize a 5e Party. Optimize for fun, that is.

[Shining Wrath]

In case the title isn't clear, what I want from you is a brief sketch of a party you think would be fun to be part of. I'm looking for classes / backgrounds / races, not "I want to play with Neil DeGrasse Tyson and 2 Supermodels".

Around level 5 if it matters, where your characters are just starting to come into their own.

I'll start.

I'll play an Oath of Vengeance Paladin, a Tiefling with a grudge against the people who slaughtered his clan of traveling merchants.
Companion #1: A noble born High Elf who has become a Warlock with a Pact with an Outsider and is so preoccupied with the other world that he barely notices this one, until it's time for combat, which focuses his mind wonderfully.
Companion #2: Human rogue on the run from his erstwhile gang of assassins, trying to redeem his bloody past by aiding me in my vengeance.
Companion #3: A Dwarf bard, a skilled lute player whose family and clan never understood (or tolerated) his preference for music over smithing and mining. Has a, shall we say, soft spot for females unadorned with beards.

[VoxRationis]

A human Barbarian with the Sage background, learned in lore but exiled for his violent and destructive tendencies, which surface unexpectedly from his normally meek personality.

A halfling Paladin whose quest is to improve the image of halflings everywhere, such that they are not thought of automatically as thieves. Hates even minor acts of thievery and will not condone them.

An Assassin-archetype rogue who believes in never killing without careful consideration of both moral and practical consequences. Frequently uses disabling or nonlethal weapons.

A grizzled old ex-Soldier dwarven wizard whose career in the arcane was set back many years by his compulsory military service. Somewhat wishes he had been born an elf, so that he could have been left to his studies in peace.

A bard of the Sage background, sent out by his master to determine why bards can now suddenly act as full casters rather than just dabblers in magic.

[T.G. Oskar]

The concepts for a fun party are easy to do. The problem would be the races.

I'm going for a "obvious at first, but with a secret" theme, using mostly "hybrid" classes. I'll say the theme, and you can probably figure which would be the four races. As a hint, only one appears in the Player's Handbook (the reason why I'd say the problem would be the races).

The first, and the one I'd play (obviously) is an LG Devotion Paladin. A sword & boarder, questing to fight against the forces of evil and spread the beauty of chivalry. Probably Noble background, to hammer the point of being chivalrous. A Knight-Errant, of sorts. The secret? Well, she is cursed with lycanthropy, and while she struggles against it, she secretly wishes to harness and embrace this power. However, the kingdom (or church) where she belongs has a thing for lycanthropes. One of the particular reasons is because her urges are in line with her beliefs, but she fears the loss of control this would imply (the particular "breed" would be Werebear, which is naturally LG). Thus, she keeps it a secret and only uses said power when the need is dire.

One of her companions would be a CN Fiendish Warlock. The idea between the Paladin and the Warlock would be "vitriolic best buds"; they can't stand each other, and are constantly bickering, but collaborate because they're on the same "theme". The Warlock wouldn't be a "Chaotic Stupid" guy; somewhat amoral, yes, but driven to collaborate if needed. Having the Criminal background and maybe the Beguiling Influence invocation, he'd be the face and maybe the party trap-monkey. Of course, he'd be a bit of a loner, trying to keep distance between himself and the party at every possible instance. The secret? The "charismatic cool loner antihero" attitude he projects is a facade. He's incredibly insecure of himself, somewhat jealous of the Paladin but mostly because he sees in her the confidence he desperately lacks; he doesn't make deep connections because he fears the source of his powers. He knows he's gonna fall down to the Nine Hells like a meteor, but he's deathly afraid that he drags someone else with him. Part of why he tolerates the Paladin despite the bickering and the jealousy is because he sees in her someone who, no matter what, will be capable of standing tall, and he secretly entrusts in her the duty of annihilating him if he were to drag someone to the Lower Planes with him.

The other companion would be a grizzled TN Hunter Ranger, obviously specializing in Archery (no background for him, I'm afraid, at this moment, but a nature-inclined one would be nice). Self-sufficient, and very resource-conscious. No-nonsense guy, efficient at doing his job. The oldest of the party, and to an extent the wisest, having to serve as the mediator between the Paladin and the Warlock. His nickname would be "Bear", because he's built almost like one (big, pretty strong, but still dextrous) and his attitude is similar to one. The secret is bound to the Paladin, mostly: he has a profound hatred of lycanthropes, to the extent of going "kill on sight" for them. He knows the Paladin is a lycanthrope from the very beginning, and the reason he remains with the party is because he wants to be there to slay her at the moment she goes out of control. The Ranger has a blind hatred, and doesn't care if some lycanthropes are more benign than other (even werebears!)

The last companion would be a short and friendly NG Lore Bard, probably with the Entertainer background (did I got it right?). "Friendly" is understating it; he's incredibly friendly, to "Stupid Good" degrees. Naturally friendly to animals, almost as much as humanoids. Saying more from him would be spoiling a lot, and I feel I already spoiled a lot.

The Paladin would be an Aasimar, or the equivalent of one (Deva?). An Aasimar Paladin would be incredibly obvious, particularly for the choice of Charisma (or Wisdom?) and its Celestial heritage. The Werebear spin would be interesting though, particularly in a place like Eberron where the Silver Flame would be the definite choice, as they're fiercely against lycanthropes, enough to initiate the Purge to exterminate them.

The Warlock would naturally be a Tiefling. It should be obvious from the Fiend pact. It's also obvious that they're the "rebel" race, and this is playing to that. However, the spin plays on an unusual take on the racial rebellion of the character; he faces the forces of darkness using the same weapons because he's deathly afraid of them, and he's deathly afraid of his own power. He has to lie and form a mask to cover this fear. Also: remember I said one of the races would be from the PHB?

The Ranger would be a Shifter, which are pretty self-sufficient and have animalistic features. Shifters are said to descent from lycanthropes, so in a way, Bear would be attempting to purge a part of himself. His resemblance to a Bear would be due to his heritage; he looks a lot like a bear, so people call him Bear, and his attitude just happens to match. Sort of a way to play with the theme of racism and how someone can be judgmental and still reconsider the situation.

As for the Bard...if you got the little clues, you should figure he'd be a Kender. Kender are naturally friendly and childishly innocent. Thus, the secret has to break a bit from that idea, and thus, it's the only spoilered surprise: while genuinely good, he's not beyond using his childlike appearance and demeanor to his benefit. I said Entertainer, but he'd fit right into Charlatan, conning and swindling his way out of people. The main difference, and what keeps him grounded in Neutral Good attitude, is that he doesn't con and swindle out of a monetary interest; he perceives it as a game, and one where he likes to have the advantage. The best way to put is is having a gambler who cheats like crazy to win, but doesn't care a whit about the prize; the very act of winning is enough. Dangerously close to being Afflicted, sure, but still grounded into goodness. He wouldn't trick his friends, but he has a nasty streak when someone tricks his "friends", which is where his dangerous inclination towards Affliction freely manifests. This would require a master roleplayer, because it's an intense character who can easily be played wrong.

[UHF]

In terms of play, mobility goes a long way. Creating a team that pushes baddies around and is able to take advantage of the gaps created is way fun.

I ran a 4e conversion of Terror In Freeport and all the characters emphasized stealth and mobility. In a city environment combat went 3D more often than not. The Goblin Rogue was up the walls, and the monk was making some mighty cool leaps.

Our 5e Party has a similar build. All stealth capable, and strong and mobile.

[Logosloki]

Everyone as half-elves with the Sailor:pirate Background. Personality trait To me, a tavern brawl is a nice way to get to know a new city, Ideal Fairness, Bond is Ruthless pirates murdered my captain and crew mates, plundered our ship, and left me to die, Vengeance will be mine and Flaw is I can’t help but pocket loose coins and other trinkets I come across. If you are allowed a Feat it has to be tavern brawler.

You are the survivors of a group of corsairs whose ship was scuttled in a coup. While you don't have a ship any more, you have each other and in a world which hates your hybrid nature that brings you together as much as your mutual hatred for the scurvy dogs who scuttled your ship. Your goal as a group is to gather up enough people to make and crew a pirate ship again and sail off into the sunset - much to the chagrin of your DM. You go from city to city much like you used to go port to port, drinking, singing, fighting and wenching.