5e doesn't use BAB. Classes that have the extra attack ability get a second attack at level 5. That would be fighters, paladins, rangers, barbarians, monks, and warlocks using the thirsting blade invocation. Bards in the college of valor get extra attack at level 6. Anyone can dual wield using light weapons, using a bonus action to make an offhand attack, but I haven't tested how that works in the game. Fighters get a 3rd attack at level 11, and fourth attack at level 20. Monks have a specialized version of dual wielding using unarmed strikes called martial arts, but it requires using a bonus action to make the unarmed attack. Some feats can grant extra attacks, such as polearm master which allows you to make an attack with the butt of a polearm style weapon using a bonus action.
This. But also a few small additions. Dual wielding allows for off hand attacks using a bonus action, but only smaller weapons (shortsword or smaller) allow dual wielding. Fighters get Action Surge at lvl 2, which allows for an extra action oncer per short or long rest. Barbarians may get Frenzy, which allows them an extra attack as a bonus action when they are under the effects of Rage (can be used up to 3 times per long rest at lv 3). Colossus Slayer and Horde Breaker both give a ranger extra attacks/ sources of damage.
