New answers tagged fighting-style
A character's Proficiency Bonus and the Fighter's Fighting Style class feature do stack. Proficiency with something in 5e allows you to add your Proficiency Bonus to the relevant rolls. This is a dynamic bonus that scales with character level (not class level) and caps at +6 at level 20. Archery is a static +2 bonus to attack rolls made with ranged weapons ...
Both of those modifiers do add to the attack roll; the combined modifier is then relevant ability mod (DEX, +3) + proficiency bonus (+2) + Archery bonus (+2), yielding the +7 you see in the "Attacks & Spellcasting" section of the pregen character sheet.
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