The Battle of Five Armies was a battle waged between the Goblins and the Wargs against Men of Dale, Elves, Dwarves, Eagles and a Shape-shifter on and near the Lonely Mountain.
I love the above quote taken from the OneRing wiki because it identifies so much of the confusion around the current film.
"Who are the five armies?"
Do you know how many people got this right?
And you did not either. Don't kid yourself...Nobody seeing the films says Goblins.
You said Orcs. Because, well there is an Army of Orcs. In fact, in the film there are two. Real live armies, with different ranks, roles, and skills--clearly and visually portrayed multiple times. More importantly the Goblins involved in the final battle seem to number about 100 and are killed rather quickly by two dwarfs & maybe a hobbit hurling rocks. Hardly an Army of Goblins.
In the films, the Wargs are just orcs--they have about as many lines as your standard unnamed orc. There are likely fewer Wargs then there are Spiders--and they likely mean less. There is clearly not an Army of Wargs. No one says Wargs.
The Men of Dale are an army of sorts, more like a defensive militia, but they do fight skirmishes with leaders--they exhibit command and control behavior. The have rank and role. Most people name Men as an Army.
The Army of Dwarfs (I know, I know--OneRing is wrong) in the film is really two armies--and one is more of a band. But overall, must people guess this and are correct.
The Army of Elves is the most obvious army & everyone says this and they are Right. The Elfish (again, I know, I know--everyone is wrong) Army along with the Orcs is clearly the most organized and traditionally military.
Some people say Eagles. Generally this is just a guess to get to five. There are very few Eagles even though the once again save the day. Even in the book, I am no sure you can count the Eagles as an army--Tolkien's War Trauma clearly impacted this inclusion.
The Shape Shifter's are not an Army. No one guesses this. Ever. Even in the film, the Army of One is more like a military tool than a unique military organization--roughly on par with the wall smashing Mountain Troll.
So who are the five Armies? I think that the answer is that no one really knows, but the film argues for a very different set then what is traditionally counted.