5. { (x - 2)/3 - (x + 1)/2 >= 1, 4x - 3(2x - 1) > 5 }

Step 1: Solve the first inequality: (x - 2)/3 - (x + 1)/2 >= 1. Multiply by 6: 2(x - 2) - 3(x + 1) >= 6 => 2x - 4 - 3x - 3 >= 6 => -x - 7 >= 6 => -x >= 13 => x <= -13.

Step 2: Solve the second inequality: 4x - 3(2x - 1) > 5 => 4x - 6x + 3 > 5 => -2x + 3 > 5 => -2x > 2 => x < -1.

Step 3: Find the intersection of the solutions. Since x <= -13 and x < -1, the common solution is x <= -13.

Answer: x <= -13.