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What kind of attack bonus does a level 1 sorcerer have with a light crossbow in D&D 5e?

While teaching my siblings the basics of D&D, one of them decided to create, as a first character, a Dragonborn Sorcerer. One of the Sorcerer's proficiencies is with light crossbows, and is part of their starting equipment.

> PROFICIENCIES  
**Armor**: None  
**Weapons**: Daggers, darts, slings, quarterstaffs, light crossbows  
**Tools**: None  
<sub>(PBH)</sub>

The section on weapon proficiency says:

> Proficiency with a weapon allows you to add your proficiency bonus to the attack roll for any attack you make with that weapon.

Since sorcerers are proficient in light crossbows, this would mean that at level 1, there's a +2 to hit for a sorcerer using this weapon.

However, I recall seeing somewhere that you also add your Dexterity modifier to the attack roll for a light crossbow. I can't find this in the Player's Handbook, however. 

Am I imagining this? What kind of attack bonuses does a sorcerer have with a light crossbow at level 1? (Is there a damage bonus besides the 1d8 that I'm forgetting about?)