To solve the equation \( 3x - 5 = -17 \) by adding 5 to both sides, you proceed as follows:
Starting with the equation: \[ 3x - 5 = -17 \]
Add 5 to both sides: \[ 3x - 5 + 5 = -17 + 5 \]
This simplifies to: \[ 3x = -12 \]
So, after adding 5 to both sides of the equation, you get: \[ 3x = -12 \]