To solve the inequality \(|3x - 1| < |2x + 5|\), we consider the cases for the absolute values.

Case 1: Both expressions are positive or both are negative.

1. Solve \(3x - 1 = 2x + 5\):

\(3x - 2x = 5 + 1\)

\(x = 6\)

2. Solve \(3x - 1 = -(2x + 5)\):

\(3x - 1 = -2x - 5\)

\(3x + 2x = -5 + 1\)

\(5x = -4\)

\(x = -\frac{4}{5}\)

Thus, the solution is \(-\frac{4}{5} < x < 6\).