|x-3|=5

To solve the equation \(|x - 3| = 5\), we need to consider the two cases for the absolute value.

1. Case 1: \(x - 3 = 5\)

   \[ x - 3 = 5 \]

   Adding 3 to both sides:

   \[ x = 5 + 3 = 8 \]

2. Case 2: \(x - 3 = -5\)

   \[ x - 3 = -5 \]

   Adding 3 to both sides:

   \[ x = -5 + 3 = -2 \]

Therefore, the solutions to the equation \(|x - 3| = 5\) are:

\[ x = 8 \quad \text{and} \quad x = -2 \]