Imagine what the graph would look like. Does it open upwards or downwards?
5x - 1 has a positive slope of 5 and it is reflected horizontally. The graph would be shaped like a V. A limited segment, or none, of the graph is below a certain value of y, and the rest outside it is above.
Hence, the solution must be a < x < b.
|5x - 1| < 1
5x - 1 < 1
x < 2/5
|5x - 1| < 1
5x - 1 > -1
x > 0
0 < x < 2/5