How many attacks can a fighter with two-weapon fighting make at 5th level?
3 attacks, that's the answer.
It could go up to five with Action Surge, though.
Let's detail it:
Two-Weapon Fighting (PHB, page 195)
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative. If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.
A bonus action is different from an Action.
When you are a 5th level fighter and you take the Attack action, you can make two attacks. You can also use your bonus action to make an additional attack and you only add your ability modifier to that damage if you have the Two-Weapon Fighting style.
Two-Weapon Fighting (PHB, page 72)
When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack.
Therefore you are making your Attack action (2 attacks) and then your bonus action (1 attack) having then a total of 3 attacks if you're using your Action plus your Bonus Action. There's a clear difference between them.
Action Surge lets a 5th level fighter attack 5 times.
Action Surge (PHB, page 72)
Starting at 2nd level, you can push yourself beyond your normal limits for a moment. On your turn, you can take one additional action on top of your regular action and a possible bonus action. Once you use this feature, you must finish a short or long rest before you can use it again. Starting at 17th level, you can use it twice before a rest, but only once on the same turn.
Which means you would have 2 actions and still have your bonus action. So with this you can take your Attack action (2 attacks), then another Attack action (2 more attacks) and finally, your Two-Weapon Fighting bonus action (one more attack) making for a total of 5 attacks during your turn.
Well explained but somehow I'm still unclear. From your explanation, WITHOUT using Action Surge a 5th level fighter with Two-Weapon Fighting has two attacks as per normal. With extra attack granted at 5th level, this would only be one extra attack (with one weapon, not two). Is this correct? The Action Surge would allow the player to make an additional action which could be an attack (2 attacks for Two-Weapon Fighter) or some other action like casting a spell etc.. Have I got that right?
@Fogcutter Without using action surge, a 5th level fighter attacks 3 times as clearly explained. 2 attacks from your attack action and one attack from your bonus action. You are not granted one extra attack when you are 5th lvl. Your attack action, when you're 5th lvl, allows you to attack twice instead of once with one weapon. It doesn't matter if you have only one sword. Two-Weapon Fighting allows you to attack, using your bonus action, with your off-hand-weapon. Total of 3 attacks (Action + Bonus Action) Action Surge allows you to use Action+Action+Bonus Action (5 attacks)